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Physics Midterm Review
2012
Terms - Measurements




time elapsed = duration of an event –
there is a beginning, a middle, and an
end to any event.
distance = path length
displacement = change in position
mass = measure of inertia or
resistance to change in state of motion
Terms - Measurements




time elapsed = duration of an event –
there is a beginning, a middle, and an
end to any event.
distance = path length
displacement = change in position
mass = measure of inertia or
resistance to change in state of motion
Terms - Measurements




time elapsed = duration of an event –
there is a beginning, a middle, and an
end to any event.
distance = path length
displacement = change in position
mass = measure of inertia or
resistance to change in state of motion
Terms - Measurements




time elapsed = duration of an event –
there is a beginning, a middle, and an
end to any event.
distance = path length
displacement = change in position
mass = measure of inertia or
resistance to change in state of motion
Terms - Measurements




time elapsed = duration of an event –
there is a beginning, a middle, and an
end to any event.
distance = path length
displacement = change in position
mass = measure of inertia or
resistance to change in state of motion
Terms - Measurements




time elapsed = duration of an event –
there is a beginning, a middle, and an
end to any event.
distance = path length
displacement = change in position
mass = measure of inertia or
resistance to change in state of motion
Terms - Measurements




time elapsed = duration of an event –
there is a beginning, a middle, and an
end to any event.
distance = path length
displacement = change in position
mass = measure of inertia or
resistance to change in state of motion
Terms - Measurements




time elapsed = duration of an event –
there is a beginning, a middle, and an
end to any event.
distance = path length
displacement = change in position
mass = measure of inertia or
resistance to change in state of motion
Terms - Measurements




time elapsed = duration of an event –
there is a beginning, a middle, and an
end to any event.
distance = path length
displacement = change in position
mass = measure of inertia or
resistance to change in state of motion
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values







speed – distance as a function of time
velocity – change in position as a function of time
acceleration – change in velocity as a function of
time
centripetal acceleration – Quotient of the velocity
squared and the distance from the center of
rotation
momentum – product of mass and velocity
change in momentum = Impulse = change in the
product of mass and velocity
force = change in momentum per unit of time
Calculated Values





Weight = Force due to Gravity = product of mass and
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of mass and
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Weight = Force due to Gravity = product of massand
acceleration due to gravity
Universal Gravitational Force is directly proportional to
the universal gravitational constant, the mass of one
object, the mass of another object and inversely
proportional to the distance between the center of the
objects squared
work – product of parallel component of the force and
distance the force is applied through
Kinetic energy – product of ½ the mass and the velocity
squared
.
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Calculated Values





Power = work done per unit of time
Power = energy transferred per unit of time
Pressure= Force per unit area
Torque = product of perpendicular
component of force and distance the force is
applied to the center of rotation
moment of Inertia – sum of the product of
the mass and the distance from the center
of rotation squared
Mechanics
Final velocity = initial velocity added to the product of
the acceleration and time accelerating.
 Formula: v = vo + at
 Units: m = m + m (s)
s s
s2
 Relationships:
Therefore the final velocity is directly related to the
acceleration.
It is also directly related to the time accelerating.

Mechanics
Final velocity = initial velocity added to the product of
the acceleration and time accelerating.
 Formula: v = vo + at
 Units: m = m + m (s)
s s
s2
 Relationships:
Therefore the final velocity is directly related to the
acceleration.
It is also directly related to the time accelerating.

Mechanics
Final velocity = initial velocity added to the product of
the acceleration and time accelerating.
 Formula: v = vo + at
 Units: m = m + m (s)
s s
s2
 Relationships:
Therefore the final velocity is directly related to the
acceleration.
It is also directly related to the time accelerating.

Mechanics
Final velocity = initial velocity added to the product of
the acceleration and time accelerating.
 Formula: v = vo + at
 Units: m = m + m (s)
s s
s2
 Relationships:
Therefore the final velocity is directly related to the
acceleration.
It is also directly related to the time accelerating.

Mechanics
Final velocity = initial velocity added to the product of
the acceleration and time accelerating.
 Formula: v = vo + at
 Units: m = m + m (s)
s s
s2
 Relationships:
Therefore the final velocity is directly related to the
acceleration.
It is also directly related to the time accelerating.

Mechanics








Final position is equal to the initial position added to the
product of the initial velocity and the time elapsed and the one
half the product of the acceleration and time accelerating
squared
Formula x=xo + vot + ½ at2
Units m =m + m (s) m s2
s
s2
The displacement is equal to the product of the initial velocity
and the time elasped and the one half the product of the
acceleration and time accelerating squared
Formula Dx = vot + ½ at2
Units m =m (s) m s2
s
s2
If the initial velocity is zero the displacement is directly related
to the square of the time accelerating
Mechanics








Final position is equal to the initial position added to the
product of the initial velocity and the time elapsed and the one
half the product of the acceleration and time accelerating
squared
Formula x=xo + vot + ½ at2
Units m =m + m (s) + m s2
s
s2
The displacement is equal to the product of the initial velocity
and the time elasped and the one half the product of the
acceleration and time accelerating squared
Formula Dx = vot + ½ at2
Units m =m (s) m s2
s
s2
If the initial velocity is zero the displacement is directly related
to the square of the time accelerating
Mechanics








Final position is equal to the initial position added to the
product of the initial velocity and the time elapsed and the one
half the product of the acceleration and time accelerating
squared
Formula x=xo + vot + ½ at2
Units m =m + m (s) + m s2
s
s2
The displacement is equal to the product of the initial velocity
and the time elasped and the one half the product of the
acceleration and time accelerating squared
Formula Dx = vot + ½ at2
Units m =m (s) m s2
s
s2
If the initial velocity is zero the displacement is directly related
to the square of the time accelerating
Mechanics








Final position is equal to the initial position added to the
product of the initial velocity and the time elapsed and the one
half the product of the acceleration and time accelerating
squared
Formula x=xo + vot + ½ at2
Units m =m + m (s) + m s2
s
s2
The displacement is equal to the product of the initial velocity
and the time elapsed and the one half the product of the
acceleration and time accelerating squared
Formula Dx = vot + ½ at2
Units m =m (s) m s2
s
s2
If the initial velocity is zero the displacement is directly related
to the square of the time accelerating
Mechanics








Final position is equal to the initial position added to the
product of the initial velocity and the time elapsed and the one
half the product of the acceleration and time accelerating
squared
Formula x=xo + vot + ½ at2
Units m =m + m (s) + m s2
s
s2
The displacement is equal to the product of the initial velocity
and the time elapsed and one half the product of the
acceleration and time accelerating squared
Formula Dx = vot + ½ at2
Units m =m (s) m s2
s
s2
If the initial velocity is zero the displacement is directly related
to the square of the time accelerating
Mechanics





Final Velocity Squared equals the Initial velocity
squared added to the product of the acceleration
and the displacement.
Formula: v2 = vo2 + 2 a D x
m2 m2
mm
s2 s2
s2
Very Useful because the relationships between final
velocity, initial velocity, acceleration and
displacement can be determined without knowing
the time elasped
Mechanics





Final Velocity Squared equals the Initial velocity
squared added to the product of the acceleration
and the displacement.
Formula: v2 = vo2 + 2 a D x
m2 m2
mm
s2 s2
s2
Very Useful because the relationships between final
velocity, initial velocity, acceleration and
displacement can be determined without knowing
the time elasped
Mechanics





Final Velocity Squared equals the Initial velocity
squared added to the product of the acceleration
and the displacement.
Formula: v2 = vo2 + 2 a D x
m2 m2
mm
s2 s2
s2
Very Useful because the relationships between final
velocity, initial velocity, acceleration and
displacement can be determined without knowing
the time elasped
Mechanics





Final Velocity Squared equals the Initial velocity
squared added to the product of the acceleration
and the displacement.
Formula: v2 = vo2 + 2 a D x
m2 m2
mm
s2 s2
s2
Very Useful because the relationships between final
velocity, initial velocity, acceleration and
displacement can be determined without knowing
the time elasped
Mechanics






Vector sum of the forces is equal to the net force
which is equal to the product of the mass of the
object and its acceleration.
Formula: S F = Fnet = m a
Units:
N = kg m
s2
Noncontact – Gravitational, Electromagnetism,
Nuclear
Contact – Normal, Friction, Tension
Mechanics






Vector sum of the forces is equal to the net force
which is equal to the product of the mass of the
object and its acceleration.
Formula: S F = Fnet = m a
Units:
N = kg m
s2
Noncontact – Gravitational, Electromagnetism,
Nuclear
Contact – Normal, Friction, Tension
Mechanics






Vector sum of the forces is equal to the net force
which is equal to the product of the mass of the
object and its acceleration.
Formula: S F = Fnet = m a
Units:
N = kg m
s2
Noncontact – Gravitational, Electromagnetism,
Nuclear
Contact – Normal, Friction, Tension
Mechanics






Vector sum of the forces is equal to the net force
which is equal to the product of the mass of the
object and its acceleration.
Formula: S F = Fnet = m a
Units:
N = kg m
s2
Noncontact – Gravitational, Electromagnetism,
Nuclear
Contact – Normal, Friction, Tension
Mechanics






Vector sum of the forces is equal to the net force
which is equal to the product of the mass of the
object and its acceleration.
Formula: S F = Fnet = m a
Units:
N = kg m
s2
Noncontact – Gravitational, Electromagnetism,
Nuclear
Contact – Normal, Friction, Tension
Mechanics






Vector sum of the forces is equal to the net force
which is equal to the product of the mass of the
object and its acceleration.
Formula: S F = Fnet = m a
Units:
N = kg m
s2
Noncontact – Gravitational, Electromagnetism,
Nuclear
Contact – Normal, Friction, Tension
Mechanics


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


Force due to friction is less than or equal to the product of the
coefficient of friction and the normal force
Formula Ffr < m FN
Units
N
N
Therefore – Coefficient of friction is equal to the ratio of the
normal force to the frictional force
Formula m = Ffr
FN
Units
m = None – it is a ratio of the frictional force
to the normal force
Mechanics








Force due to friction is less than or equal to the product of the
coefficient of friction and the normal force
Formula Ffr < m FN
Units
N
N
Therefore – Coefficient of friction is equal to the ratio of the
normal force to the frictional force
Formula m = Ffr
FN
Units
m = None – it is a ratio of the frictional force
to the normal force
Mechanics








Force due to friction is less than or equal to the product of the
coefficient of friction and the normal force
Formula Ffr < m FN
Units
N
N
Therefore – Coefficient of friction is equal to the ratio of the
normal force to the frictional force
Formula m = Ffr
FN
Units
m = None – it is a ratio of the frictional force
to the normal force
Mechanics








Force due to friction is less than or equal to the product of the
coefficient of friction and the normal force
Formula Ffr < m FN
Units
N
N
Therefore – Coefficient of friction is equal to the ratio of the
normal force to the frictional force
Formula m = Ffr
FN
Units
m = None – it is a ratio of the frictional force
to the normal force
Mechanics








Force due to friction is less than or equal to the product of the
coefficient of friction and the normal force
Formula Ffr < m FN
Units
N
N
Therefore – Coefficient of friction is equal to the ratio of the
normal force to the frictional force
Formula m = Ffr
FN
Units
m = None – it is a ratio of the frictional force
to the normal force
Mechanics











Centripetal Acceleration is quotient of the velocity squared and
the radius of its path
Formula: ac = v2
r
Units
m = (m/s)2
s2
m
The magnitude of the velocity does not change
The direction of the object continually changes towards the
center of rotation
The velocity vector is directed tangent to its path
The acceleration vector is directed to the center of rotation
The force vector that causes this motion is perpendicular to the
velocity vector.
The force vector is also directed towards the center of rotation
Mechanics











Centripetal Acceleration is quotient of the velocity squared and
the radius of its path
Formula: ac = v2
r
Units
m = (m/s)2
s2
m
The magnitude of the velocity does not change
The direction of the object continually changes towards the
center of rotation
The velocity vector is directed tangent to its path
The acceleration vector is directed to the center of rotation
The force vector that causes this motion is perpendicular to the
velocity vector.
The force vector is also directed towards the center of rotation
Mechanics











Centripetal Acceleration is quotient of the velocity squared and
the radius of its path
Formula: ac = v2
r
Units
m = (m/s)2
s2
m
The magnitude of the velocity does not change
The direction of the object continually changes towards the
center of rotation
The velocity vector is directed tangent to its path
The acceleration vector is directed to the center of rotation
The force vector that causes this motion is perpendicular to the
velocity vector.
The force vector is also directed towards the center of rotation
Mechanics











Centripetal Acceleration is quotient of the velocity squared and
the radius of its path
Formula: ac = v2
r
Units
m = (m/s)2
s2
m
The magnitude of the velocity does not change
The direction of the object continually changes towards the
center of rotation
The velocity vector is directed tangent to its path
The acceleration vector is directed to the center of rotation
The force vector that causes this motion is perpendicular to the
velocity vector.
The force vector is also directed towards the center of rotation
Mechanics











Centripetal Acceleration is quotient of the velocity squared and
the radius of its path
Formula: ac = v2
r
Units
m = (m/s)2
s2
m
The magnitude of the velocity does not change
The direction of the object continually changes towards the
center of rotation
The velocity vector is directed tangent to its path
The acceleration vector is directed to the center of rotation
The force vector that causes this motion is perpendicular to the
velocity vector.
The force vector is also directed towards the center of rotation
Mechanics











Centripetal Acceleration is quotient of the velocity squared and
the radius of its path
Formula: ac = v2
r
Units
m = (m/s)2
s2
m
The magnitude of the velocity does not change
The direction of the object continually changes towards the
center of rotation
The velocity vector is directed tangent to its path
The acceleration vector is directed to the center of rotation
The force vector that causes this motion is perpendicular to the
velocity vector.
The force vector is also directed towards the center of rotation
Mechanics











Centripetal Acceleration is quotient of the velocity squared and
the radius of its path
Formula: ac = v2
r
Units
m = (m/s)2
s2
m
The magnitude of the velocity does not change
The direction of the object continually changes towards the
center of rotation
The velocity vector is directed tangent to its path
The acceleration vector is directed to the center of rotation
The force vector that causes this motion is perpendicular to the
velocity vector.
The force vector is also directed towards the center of rotation
Mechanics











Centripetal Acceleration is quotient of the velocity squared and
the radius of its path
Formula: ac = v2
r
Units
m = (m/s)2
s2
m
The magnitude of the velocity does not change
The direction of the object continually changes towards the
center of rotation
The velocity vector is directed tangent to its path
The acceleration vector is directed to the center of rotation
The force vector that causes this motion is perpendicular to the
velocity vector.
The force vector is also directed towards the center of rotation
Mechanics











Centripetal Acceleration is quotient of the velocity squared and
the radius of its path
Formula: ac = v2
r
Units
m = (m/s)2
s2
m
The magnitude of the velocity does not change
The direction of the object continually changes towards the
center of rotation
The velocity vector is directed tangent to its path
The acceleration vector is directed to the center of rotation
The force vector that causes this motion is perpendicular to the
velocity vector.
The force vector is also directed towards the center of rotation
Mechanics




The Torque is equal to the product of the force,
distance that force is applied to the center of rotation
and the sin of the angle that force is applied
Formula T = F r sin f
Units N m = N m
No work is done because the force is applied
perpendicular to the displacement
Mechanics




The Torque is equal to the product of the force,
distance that force is applied to the center of rotation
and the sin of the angle that force is applied
Formula T = F r sin f
Units N m = N m
No work is done because the force is applied
perpendicular to the displacement
Mechanics




The Torque is equal to the product of the force,
distance that force is applied to the center of rotation
and the sin of the angle that force is applied
Formula T = F r sin f
Units N m = N m
No work is done because the force is applied
perpendicular to the displacement
Mechanics




The Torque is equal to the product of the force,
distance that force is applied to the center of rotation
and the sin of the angle that force is applied
Formula T = F r sin f
Units N m = N m
No work is done because the force is applied
perpendicular to the displacement
Mechanics




The Torque is equal to the product of the force,
distance that force is applied to the center of rotation
and the sin of the angle that force is applied
Formula T = F r sin f
Units N m = N m
No work is done because the force is applied
perpendicular to the displacement
Mechanics







Momentum equals the product of the mass and the
velocity of the object
Formula p = m v
Units kg m = kg m
s
s
Momentum before equals momentum after
po=p
Called the conservation of momentum
Mechanics







Momentum equals the product of the mass and the
velocity of the object
Formula p = m v
Units kg m = kg m
s
s
Momentum before equals momentum after
po=p
Called the conservation of momentum
Mechanics







Momentum equals the product of the mass and the
velocity of the object
Formula p = m v
Units kg m = kg m
s
s
Momentum before equals momentum after
po=p
Called the conservation of momentum
Mechanics







Momentum equals the product of the mass and the
velocity of the object
Formula p = m v
Units kg m = kg m
s
s
Momentum before equals momentum after
po=p
Called the conservation of momentum
Mechanics







Momentum equals the product of the mass and the
velocity of the object
Formula p = m v
Units kg m = kg m
s
s
Momentum before equals momentum after
po=p
Called the conservation of momentum
Mechanics









Impulse equals the change in momentum equals the
product of the Force and the time that force acts.
Formula J = F D t = D p
Units
Ns = N s = kg m
s
Force equals the quotient of the change in
momentum and the time the force acts on the object
Formula F = D p
t
Units
N = kg m = kg m
s s
s2
Mechanics









Impulse equals the change in momentum equals the
product of the Force and the time that force acts.
Formula J = F D t = D p
Units
N s = N s = kg m
s
Force equals the quotient of the change in
momentum and the time the force acts on the object
Formula F = D p
t
Units
N = kg m = kg m
s s
s2
Mechanics









Impulse equals the change in momentum equals the
product of the Force and the time that force acts.
Formula J = F D t = D p
Units
N s = N s = kg m
s
Force equals the quotient of the change in
momentum and the time the force acts on the object
Formula F = D p
t
Units
N = kg m = kg m
s s
s2
Mechanics









Impulse equals the change in momentum equals the
product of the Force and the time that force acts.
Formula J = F D t = D p
Units
N s = N s = kg m
s
Force equals the quotient of the change in
momentum and the time the force acts on the object
Formula F = D p
t
Units
N = kg m = kg m
s s
s2
Mechanics







Kinetic energy equals one half the product of the
mass and the velocity squared of the object
Formula k = ½ mv2
Units
J = kg m2 = N m
s2
Relationship
The kinetic energy varies directly as the square of
the velocity
Kinetic Energy is a scalar quantity
Mechanics







Kinetic energy equals one half the product of the
mass and the velocity squared of the object
Formula k = ½ mv2
Units
J = kg m2 = N m
s2
Relationship
The kinetic energy varies directly as the square of
the velocity
Kinetic Energy is a scalar quantity
Mechanics







Kinetic energy equals one half the product of the
mass and the velocity squared of the object
Formula k = ½ mv2
Units
J = kg m2 = N m
s2
Relationship
The kinetic energy varies directly as the square of
the velocity
Kinetic Energy is a scalar quantity
Mechanics







Kinetic energy equals one half the product of the
mass and the velocity squared of the object
Formula k = ½ mv2
Units
J = kg m2 = N m
s2
Relationship
The kinetic energy varies directly as the square of
the velocity
Kinetic Energy is a scalar quantity
Mechanics







Kinetic energy equals one half the product of the
mass and the velocity squared of the object
Formula k = ½ mv2
Units
J = kg m2 = N m
s2
Relationship
The kinetic energy varies directly as the square of
the velocity
Kinetic Energy is a scalar quantity
Mechanics





Change in gravitational potential energy is equal to
the product of the objects mass, acceleration due to
gravity, and the vertical displacement of the object.
Formula D Ug = m g D y
Units
J = kg m m
s2
The gravitation potential energy equals the product
of the mass, acceleration due to gravity, and the
vertical position of the object.
Mechanics





Change in gravitational potential energy is equal to
the product of the objects mass, acceleration due to
gravity, and the vertical displacement of the object.
Formula D Ug = m g D y
Units
J = kg m m
s2
The gravitation potential energy equals the product
of the mass, acceleration due to gravity, and the
vertical position of the object.
Mechanics





Change in gravitational potential energy is equal to
the product of the objects mass, acceleration due to
gravity, and the vertical displacement of the object.
Formula D Ug = m g D y
Units
J = kg m m
s2
The gravitation potential energy equals the product
of the mass, acceleration due to gravity, and the
vertical position of the object.
Mechanics





Change in gravitational potential energy is equal to
the product of the objects mass, acceleration due to
gravity, and the vertical displacement of the object.
Formula D Ug = m g D y
Units
J = kg m m
s2
The gravitation potential energy equals the product
of the mass, acceleration due to gravity, and the
vertical position of the object.
Mechanics




Work is equal the product of the force the distance
the object moves and the cosine of the angle the
force is applied.
Formula: W = F d cos f
Units:
J = N m = kg m m
s2
Mechanics




Work is equal the product of the force the distance
the object moves and the cosine of the angle the
force is applied.
Formula: W = F d cos f
Units:
J = N m = kg m m
s2
Mechanics




Work is equal the product of the force the distance
the object moves and the cosine of the angle the
force is applied.
Formula: W = F d cos f
Units:
J = N m = kg m m
s2
Mechanics




Work is equal the product of the force the distance
the object moves and the cosine of the angle the
force is applied.
Formula: W = F d cos f
Units:
J = N m = kg m m
s2
Mechanics
















Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
















Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
















Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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


Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2 s
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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
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








Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2 s
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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

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








Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2 s
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2 s
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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











Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2 s
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2 s
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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













Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2 s
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2 s
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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
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











Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2 s
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2s
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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













Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2 s
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2s
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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













Power is equal to the quotient of the work and the time the work is done in.
Formula P = W
t
Power is equal to the quotient of the energy transferred and the time the energy is
transferred in.
Formula P =D U or D k
t
t
Units Watts = Joules = N m = kg m m
sec
s
s2 s
Power is equal to the product of the average force multiplied, the velocity of the object, and
the cos of the angle that the force is applied.
Formula P = F v cos f
Units Watts = N m = J = kg m m
s
s
s2s
Units
Work done or Energy Transferred equals the product of the Power and time the
work is done in or energy is transferred in
Formula Work = Power x time or Energy = Power x time U = P t W=Pt Dk=Pt
Units
J = = Watts sec
Mechanics
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


Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics
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







Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics
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

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







Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
Mechanics
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

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
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






Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics
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

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











Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
Mechanics

















Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
Mechanics

















Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
Mechanics


















Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics


















Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics

















Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
Mechanics

















Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
Mechanics


















Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics


















Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics


















Restorative Force of a Spring is equal to the negative product of the spring
constant and the displacement
Formula Fs = - Kx
Units
N
Nm
m
Potential energy associated with a spring is equal to one half the product of the
spring constant and the displacement squared.
Formula Us = ½ k x2
Units Joule(J) = N m2 = N m
m
The Period of Oscillation of a spring is equal to the product of 2 p and the
quotient of the square root of the mass attached to the spring and the spring
constant
Formula Ts = 2 p m
Units = sec = kg or kg m or kg m or s2
k
N
N
kg m
m
s2
The Period of Oscillation is inversely proportional to its frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics







The period of oscillation of a pendulum is equal to the product
of 2 p and the square root of the quotient of
the length of the pendulum and the acceleration due to gravity.
Formula Tp = 2 p l
Units = sec = m or s2
g
m
s2
The Period of Oscillation is inversely proportional to its
frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics







The period of oscillation of a pendulum is equal to the product
of 2 p and the square root of the quotient of
the length of the pendulum and the acceleration due to gravity.
Formula Tp = 2 p l
Units = sec = m or s2
g
m
s2
The Period of Oscillation is inversely proportional to its
frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics







The period of oscillation of a pendulum is equal to the product
of 2 p and the square root of the quotient of
the length of the pendulum and the acceleration due to gravity.
Formula Tp = 2 p l
Units = sec = m or s2
g
m
s2
The Period of Oscillation is inversely proportional to its
frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics







The period of oscillation of a pendulum is equal to the product
of 2 p and the square root of the quotient of
the length of the pendulum and the acceleration due to gravity.
Formula Tp = 2 p l
Units = sec = m or s2
g
m
s2
The Period of Oscillation is inversely proportional to its
frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics






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The period of oscillation of a pendulum is equal to the product
of 2 p and the square root of the quotient of
the length of the pendulum and the acceleration due to gravity.
Formula Tp = 2 p l
Units = sec = m or s2
g
m
s2
The Period of Oscillation is inversely proportional to its
frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics
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The period of oscillation of a pendulum is equal to the product
of 2 p and the square root of the quotient of
the length of the pendulum and the acceleration due to gravity.
Formula Tp = 2 p l
Units = sec = m or s2
g
m
s2
The Period of Oscillation is inversely proportional to its
frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics
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

The period of oscillation of a pendulum is equal to the product
of 2 p and the square root of the quotient of
the length of the pendulum and the acceleration due to gravity.
Formula Tp = 2 p l
Units = sec = m or s2
g
m
s2
The Period of Oscillation is inversely proportional to its
frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics

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




The period of oscillation of a pendulum is equal to the product
of 2 p and the square root of the quotient of
the length of the pendulum and the acceleration due to gravity.
Formula Tp = 2 p l
Units = sec = m or s2
g
m
s2
The Period of Oscillation is inversely proportional to its
frequency
Formula T = 1
f
Units sec = 1 or 1
hz
(cycle)
sec
Mechanics
The force due to gravity is equal quotient of the the
product of the universal gravitational constant the, mass of
one object, mass of a second object and the distance
between the objects squared
Formula Fg = G mm
r2
Units
N = 6.67x10-11 N m2 kg kg
kg2 m2
The Weight which equals the force due to gravity near the
surface of a planet is equal to the product of the mass and
the acceleration due to gravity
Formula W = Fg = mg
Units
N = N = kg m
s2
Mechanics
The force due to gravity is equal quotient of the the
product of the universal gravitational constant the, mass of
one object, mass of a second object and the distance
between the objects squared
Formula Fg = G mm
r2
Units
N = 6.67x10-11 N m2 kg kg
kg2 m2
The Weight which equals the force due to gravity near the
surface of a planet is equal to the product of the mass and
the acceleration due to gravity
Formula W = Fg = mg
Units
N = N = kg m
s2
Mechanics
The force due to gravity is equal quotient of the the
product of the universal gravitational constant the, mass of
one object, mass of a second object and the distance
between the objects squared
Formula Fg = G mm
r2
Units
N = 6.67x10-11 N m2 kg kg
kg2 m2
The Weight which equals the force due to gravity near the
surface of a planet is equal to the product of the mass and
the acceleration due to gravity
Formula W = Fg = mg
Units
N = N = kg m
s2
Mechanics
The force due to gravity is equal quotient of the the
product of the universal gravitational constant the, mass of
one object, mass of a second object and the distance
between the objects squared
Formula Fg = G mm
r2
Units
N = 6.67x10-11 N m2 kg kg
kg2 m2
The Weight which equals the force due to gravity near the
surface of a planet is equal to the product of the mass and
the acceleration due to gravity
Formula W = Fg = mg
Units
N = N = kg m
s2
Mechanics
The gravitational potential energy is equal quotient of the product of the
universal gravitational constant the, mass of one object, mass of a
secondobject and the distance between the objects
Formula Ug = G mm
r
Units Joules= 6.67x10-11 N m2 kg kg = N m
kg2 m
The gravitational potential energy near the surface of a planet is equal to
the product of the mass and the acceleration due to gravity and
the vertical position of the object.
Formula Ug = m g y
Units:Joules = kg m m= N m
s2
Mechanics
The gravitational potential energy is equal quotient of the product of the
universal gravitational constant the, mass of one object, mass of a
secondobject and the distance between the objects
Formula Ug = G mm
r
Units Joules= 6.67x10-11 N m2 kg kg = N m
kg2 m
The gravitational potential energy near the surface of a planet is equal to
the product of the mass and the acceleration due to gravity and
the vertical position of the object.
Formula Ug = m g y
Units:Joules = kg m m= N m
s2
Mechanics
The gravitational potential energy is equal quotient of the product of the
universal gravitational constant the, mass of one object, mass of a
secondobject and the distance between the objects
Formula Ug = G mm
r
Units Joules= 6.67x10-11 N m2 kg kg = N m
kg2 m
The gravitational potential energy near the surface of a planet is equal to
the product of the mass and the acceleration due to gravity and
the vertical position of the object.
Formula Ug = m g y
Units:Joules = kg m m= N m
s2
Mechanics
The gravitational potential energy is equal quotient of the product of the
universal gravitational constant the, mass of one object, mass of a
secondobject and the distance between the objects
Formula Ug = G mm
r
Units Joules= 6.67x10-11 N m2 kg kg = N m
kg2 m
The gravitational potential energy near the surface of a planet is equal to
the product of the mass and the acceleration due to gravity and
the vertical position of the object.
Formula Ug = m g y
Units:Joules = kg m m= N m
s2
Mechanics
The gravitational potential energy is equal quotient of the product of the
universal gravitational constant the, mass of one object, mass of a
secondobject and the distance between the objects
Formula Ug = G mm
r
Units Joules= 6.67x10-11 N m2 kg kg = N m
kg2 m
The gravitational potential energy near the surface of a planet is equal to
the product of the mass and the acceleration due to gravity and
the vertical position of the object.
Formula Ug = m g y
Units:Joules = kg m m= N m
s2
Mechanics Lab Experiences

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Run Out Back– time,distance, displacement, speed,
velocity, acceleration are dependent on:
measurements of:
distance traveled or displacement,
time elapsed
vs = d
v = Dx a = v - vo
t
t
t
Mechanics Labs-Graphical
Analysis

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Vertical Jump Lab
Cart up and Down Incline
Position as a function of time graphs
Velocity as a function of time graphs
Acceleration as a function of time graphs
V
x
t
a
t
Constant,stopped
t
Kinematic Equations Projectiles
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Horizontal motion of a cart
Vertical motion of dropped object
Horizontally fired projectile vox=vx=vocosf
Ground to ground fired projectile voy=vosinf
X and Y positions as a function of time
Y and X positions at maximum height
Ground to cliff firing
Cliff to ground firing
Kinematic Equations – Graphical and
Analytic Solutions – Vector Quanitites

Force Table
X comp Y comp
Sum of x Sum of y
Resultant – Pythagorean theorem
Tan y/x – Direction of resultant

Tip to tail – Graphical analysis

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Dynamics
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Fan Cart F=ma
Cart Pulley Falling Mass
mfg = a
(mc + mf)
Block Pulley Falling Mass
mfg - mmcg= a
(mc + mf)
Cart on incline mgsinf = Fparallel mgcosf=Fperpendicular
Block on Incline mgsinf = mmgcosf=Ffriction
Stationary block on incline mmgcosf= mgsinf
Elevator lab-at rest, constant up, constant down
accelerating up, coming to rest down
accelerating down, coming to rest up
Object 1 Pulley Heavier Object 2
mhg
=a
( mh +ml)
Cart , Block on incline Pulley Falling Mass
Uniform Circular Motion
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Ball on String
2pr(rev) =v mv
t
Coin on Turntable
Penny on Rotating Wall
Car in hot wheel track
Interactive Physics:
 Earth Satellite
 Earth Satellite Moon
 Earth Geostationary Satellite Moon
 Sun Earth Satellite Moon System
 Bipolar Star System
Work / Energy / Power
D Ug mgy–mgyo Dk = ½ mv2- ½ mvo 2 DUs = ½ kx2 -½ kxo2
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Spring Cart Lab: E.P.E. to K.E. ½ kx2 = ½ mv2
Cart on Incline: G.P.E. to K.E. lab mgDy = ½ mv2
Rollercoaster Interactive Physics: G.P.E. to K.E. lab
Bow Lab : Work to E.P.E. to K.E. Force varies with
distance = Work equals area under Force vs distance
Power Lab: Wrist Roll, Sprint, Stair Climb
P = mgDy P = Dk = ½ mv2- ½ mvo 2
Dt
Dt
Electric Motor: P = IV and Poutput =D K.E +D G.P.E
Dt
Trampoline Interactive Physics: G.P.E. to K.E to E.P.E –
G.P.E
Conservation of Momentum
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Elastic Collision of light onto stationary heavy
mLvoL = mLvL + mHv bounce back go forward po=p ko=k
Elastic Collision of heavy onto stationary light
mHvoH = mHvH + mLvL both go forward
po=p ko=k
Elastic Collision of heavy onto stationary heavy
mH1voH1 = mH2vH2 stop and go
po=p ko=k
Elastic Head on Collisions of light onto light
mLvoL1 + mLvoL2 = mLvL1 + mLvL2 switch
po=p ko=k
Inelastic collision of light onto stationary heavy
mLvoL = (mL+ mH) vLH Stick
po=p ko> k
Inelastic collision of heavy onto stationary light
mHvoH = (mH+ mL) vHL Stick
po=p ko>k
Conservation of Momentum
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Off center Collisions
pox = px and poy = py If you start with only x momentum
then any y momentum generated in one particle must be
cancelled by the y momentum of another particle.
Ballistic Sled
Momentum conservation
energy conservation
mvob = ( mb + ms)vbs
½ (mb + ms)vbs2= m(mb + ms)gd
Ballistic Pendulum
Momentum conservation
energy conservation
mvob = ( mb + mp)vbp
½ (mb + mp)vbp2= (mb + ms)gDy
Impulse Change in Momentum
Impulse = J = FD t =Change in momentum in N s = Area under the curve
F
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t
t
t
t
Stiff Spring
Soft Spring
Rubber Bumper
Magnetic bumper
Force as a function of time graph analysis
Rocket Thrust Analysis
Newton's Third Law Connection to Change in momentum
Torque

Interactive Physics
Force applied at different distances from the center of rotation

Force applied at different angles

Clockwise and Counterclockwise Torque Problems

?
Moment of Inertia – Rotational Inertia



Momentum of Inertia Demonstrations with
rotating disk and rotating loop on an incline
Balancing objects that are close to the center of
rotation
Balancing objects further from the center of
rotation
Periodic Motion
Tp = 2 p l
g



Ts = 2 p m
k
Simple harmonic motion of springs – interactive physics
Simple harmonic motion of pendulums –
Interactive physics
Fluid Dynamics
Pressure
Pascals Principle
Bouyant force
Fluids
Can be
Liquids
Gases
Because they can
Flow
Fluids
Can be
Liquids
Gases
Because they can
Flow
Fluids
Can be
Liquids
Gases
Because they can
Flow
Fluids
Can be
Liquids
Gases
Because they can
Flow
Fluid Pressure
Scalar quantity
Force acting perpendicular to and
distributed over a surface, divided by the
area of that surface
P= F
 A
Fluid Pressure
Scalar quantity
Force acting perpendicular to and
distributed over a surface, divided by the
area of that surface
P= F
 A
Fluid Pressure
Scalar quantity
Force acting perpendicular to and
distributed over a surface, divided by the
area of that surface
P= F
 A
Fluid Pressure
Scalar quantity
Force acting perpendicular to and
distributed over a surface, divided by the
area of that surface
P= F
 A
Fluid Pressure
Scalar quantity
Force acting perpendicular to and
distributed over a surface, divided by the
area of that surface
P= F
 A
Fluid Pressure
Scalar quantity
Force acting perpendicular to and
distributed over a surface, divided by the
area of that surface
P= F
 A
Fluid Pressure
Scalar quantity
Force acting perpendicular to and
distributed over a surface, divided by the
area of that surface
P= F
 A
Fluid Pressure
Scalar quantity
Force acting perpendicular to and
distributed over a surface, divided by the
area of that surface
P= F
 A
Scalar Pressure
Pressure has magnitude but no
Direction.
The force exerted by a fluid at rest is
always perpendicular to that surface
P = F = Pascals = N = kg m = kg

A
m2
m2s2 m s2
Scalar Pressure
Pressure has magnitude but no
Direction.
The force exerted by a fluid at rest is
always perpendicular to that surface
P = F = Pascals = N = kg m = kg

A
m2
m2s2 m s2
Scalar Pressure
Pressure has magnitude but no
Direction.
The force exerted by a fluid at rest is
always perpendicular to that surface
P = F = Pascals = N = kg m = kg

A
m2
m2s2 m s2
Scalar Pressure
Pressure has magnitude but no
Direction.
The force exerted by a fluid at rest is
always perpendicular to that surface
P = F = Pascals = N = kg m = kg

A
m2
m2s2 m s2
Scalar Pressure
Pressure has magnitude but no
Direction.
The force exerted by a fluid at rest is
always perpendicular to that surface
P = F = Pascals = N = kg m = kg

A
m2
m2s2 m s2
Scalar Pressure
Pressure has magnitude but no
Direction.
The force exerted by a fluid at rest is
always perpendicular to that surface
P = F = Pascals = N = kg m = kg

A
m2
m2s2 m s2
Scalar Pressure
Pressure has magnitude but no
Direction.
The force exerted by a fluid at rest is
always perpendicular to that surface
P = F = Pascals = N = kg m = kg

A
m2
m2s2 m s2
Scalar Pressure
Pressure has magnitude but no
Direction.
The force exerted by a fluid at rest is
always perpendicular to that surface
P = F = Pascals = N = kg m = kg

A
m2
m2s2 m s2
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
P= F = mg = r V g =r Ah g = r gh
 A
A
A
A
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
P= F = mg = r V g =r Ah g = r gh
 A
A
A
A
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
P= F = mg = r V g =r Ah g = r gh
 A
A
A
A
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
P= F = mg = r V g =r Ah g = r gh
 A
A
A
A
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
P= F = mg = r V g =r Ah g = r gh
 A
A
A
A
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
P= F = mg = m g h =mgh = r gh
 A
A
Ah V
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
 P= F = mg = mgh r V g =r Ah g = r gh

A
A Ah
A
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
 P= F = mg = mgh r V g =r Ah g = r gh

A
A Ah
A
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
 P= F = mg = mgh = mgh =r gh =

A
A Ah
V
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
 P= F = mg = mgh = mgh =r gh =

A
A Ah
V
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
 P= F = mg = mgh = mgh =r gh

A
A Ah
V
P = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
 P= F = mg = mgh = mgh =r gh

A
A Ah
V
Pguage = r gh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
 P= F = mg = mgh = mgh =r gh

A
A Ah
V
Pguage = r gh
Pabsolute = Poatmosphere + rgh
Gravity and Pressure
Fg = mg
r=m
V
V = Ah (for a cylinder)
 P= F = mg = mgh = mgh =r gh

A
A Ah
V
Pguage = r gh
Pabsolute = Po(atmosphere) + rgh
Pressure In a Container
The pressure at every point at a given
horizontal level in a single body of fluid at
rest is the same.

_____ pressure


_____ pressure
Pressure In a Container
The pressure at every point at a given
horizontal level in a single body of fluid at
rest is the same.

Low pressure


High pressure
Pressure In a Container
The pressure at every point at a given
horizontal level in a single body of fluid at
rest is the same.

Low pressure


High pressure
Pressure In a Container
The pressure at every point at a given
horizontal level in a single body of fluid at
rest is the same.

Low pressure


High pressure
Pascals Principle
An external pressure applied to a fluid
confined within a closed container is
transmitted…
undiminished throughout the entire fluid
Pascals Principle
An external pressure applied to a fluid
confined within a closed container is
transmitted…
undiminished throughout the entire fluid
Hydraulic Lifts
Fo = F Force output = Force input
Ao A Area output
Area input
large output force = small input force
large output area = small input area
Ao =y (y=piston displacement)
A yo
Hydraulic Lifts
Fo = F Force output = Force input
Ao A Area output
Area input
large output force = small input force
large output area = small input area
Ao =y (y=piston displacement)
A yo
Hydraulic Lifts
Fo = F Force output = Force input
Ao A Area output
Area input
large output force = small input force
large output area = small input area
Ao =y (y=piston displacement)
A yo
Hydraulic Lifts
Fo = F Force output = Force input
Ao A Area output
Area input
large output force = small input force
large output area = small input area
Ao =y (y=piston displacement)
A yo
Hydraulic Lifts
Fo = F Force output = Force input
Ao A Area output
Area input
large output force = small input force
large output area = small input area
Ao =y (y=piston displacement)
A yo
Hydraulic Lifts
Fo = F Force output = Force input
Ao A Area output
Area input
large output force = small input force
large output area = small input area
Ao =y (y=piston displacement)
A yo
Hydraulic Lifts
Fo = F Force output = Force input
Ao A Area output
Area input
large output force = small input force
large output area = small input area
Ao =y (y=piston displacement)
A yo
Bouyancy
P=F
A
FB = A P2 – A P1
FB = A(r gh) h= height of the object
FB = r gAh = r gV
Bouyancy
P=F
A
FB = A P2 – A P1
FB = A(r gh) h= height of the object
FB = r gAh = r gV
Bouyancy
P=F
A
FB = A P2 – A P1
FB = A(r gh) h= height of the object
FB = r gAh = r gV
Bouyancy
P=F
A
FB = A P2 – A P1
FB = A(r gh) h= height of the object
FB = r gAh = r gV
Bouyancy
P=F
A
FB = A P2 – A P1
FB = A(r gh) h= height of the object
FB = r gAh = r gV
Bouyancy
P=F
A
FB = A P2 – A P1
FB = A(r gh) h= height of the object
FB = r gAh = r gV
Bouyancy
P=F
A
FB = A P2 – A P1
FB = A(r gh) h= height of the object
FB = r gAh = r gV
Bouyancy
FB = r gAh = r gV
FB = r Vg = m V g
V
FB = mg =weight of fluid displaced
An object immersed in a fluid will be lighter
(buoyed up) by an amount equal to the weight of
the fluid it displaces.
Bouyancy
FB = r gAh = r gV
FB = r Vg = m V g
V
FB = mg =weight of fluid displaced
An object immersed in a fluid will be lighter
(buoyed up) by an amount equal to the weight of
the fluid it displaces.
Bouyancy
FB = r gAh = r gV
FB = r Vg = m V g
V
FB = mg =weight of fluid displaced
An object immersed in a fluid will be lighter
(buoyed up) by an amount equal to the weight of
the fluid it displaces.
Bouyancy
FB = r gAh = r gV
FB = r Vg = m V g
V
FB = mg =weight of fluid displaced
An object immersed in a fluid will be lighter
(buoyed up) by an amount equal to the weight of
the fluid it displaces.
Streamline Flow
Characterized by
________path
Path called a________
Streamlines ________cross
Equation of Continuity
Equation of Continuity
Volume
in
Equation of Continuity
Volume
out
Volume
in
Volume in = Rate In
time
A 1 h2
t
A 1 v1
= Rate Out = Volume out
time
A 2 h2
t
A 2 v2
Equation of Continuity
A1 v1 = A2v2
The product of any cross-sectional area
of the pipe and the fluid speed at that
cross-section is constant. Conservation of
matter.
Equation of Continuity
A1 v1 = A2v2
The product of any cross-sectional area
of the pipe and the fluid speed at that
cross-section is constant. Conservation of
matter.
Equation of Continuity
A1 v1 = A2v2
The product of any cross-sectional area
of the pipe and the fluid speed at that
cross-section is constant. Conservation of
matter.
Equation of Continuity
 A1 v1 = A2v2
The condition Av = a constant is equivalent to the
fact that the amount of fluid that enters one end
of the tube in a given time interval
________the amount of fluid leaving the tube
in the same interval assuming the absence of
leaks.
Equation of Continuity
 A1 v1 = A2v2
The condition Av = a constant is equivalent to the
fact that the amount of fluid that enters one end
of the tube in a given time interval equals the
amount of fluid leaving the tube in the same
interval assuming the absence of leaks.
Bernoulli's Equation
1738 Daniel Bernoulli derived an equation
that related
________and ________to
Fluid pressure
It is an equation based on the
Conservation of________
Bernoulli's Equation
1738 Daniel Bernoulli derived an equation
that related
Fluid speed and elevation to
fluid pressure
It is an equation based on the
conservation of energy
Bernoulli's Equation
1738 Daniel Bernoulli derived an equation
that related
Fluid speed and elevation to
fluid pressure
It is an equation based on the
conservation of energy
Bernoulli's Equation
1738 Daniel Bernoulli derived an equation
that related
Fluid speed and elevation to
fluid pressure
It is an equation based on the
conservation of energy
Bernoulli's Equation
1738 Daniel Bernoulli derived an equation
that related
Fluid speed and elevation to
fluid pressure
It is an equation based on the
conservation of energy
Bernoulli's Equation
1738 Daniel Bernoulli derived an equation
that related
Fluid speed and elevation to
fluid pressure
It is an equation based on the
conservation of energy
Bernoulli's Equation
1738 Daniel Bernoulli derived an equation
that related
Fluid speed and elevation to
fluid pressure
It is an equation based on the
conservation of energy
Bernoulli's Equation
Elevated Large cross sectional area
Small cross sectional area
Bernoulli's Equation
P =
V =
W1 =
W2 =
Bernoulli's Equation
P = F

A
V =
W1 =
W2 =
Bernoulli's Equation
P = F

A
V = Ah
W1 =
W2 =
Bernoulli's Equation
P = F

A
V = Ah
W1 = F1 h = P1 A1 h1 = P1 V
W2 =
Bernoulli's Equation
P = F

A
V = Ah
W1 = F1 h = P1 A1 h1 = P1 V
W2 = F2 h2 = P2 A2 h2 = P2 V
Bernoulli's Equation
W2 =
W =
Work goes into changing the gravitational
potential energy and part goes into
changing the kinetic energy
Bernoulli's Equation
W2 = F2 h2 = P2 A2 h2 = P2 V
W =
Work goes into changing the gravitational
potential energy and part goes into
changing the kinetic energy
Bernoulli's Equation
W2 = F2 h2 = P2 A2 h2 = P2 V
W = P1 V – P2 V
Work goes into changing the gravitational
potential energy and part goes into
changing the kinetic energy
Bernoulli's Equation
P1 V – P2 V = ½ mv22 – ½ mv12 + mgy2 – mgy1
Divide each term by ________to get
P1 – P2 = ½ r v22 – ½ rv12 + rgy2 – rgy1
Bernoulli's Equation
P1 V – P2 V = ½ mv22 – ½ mv12 + mgy2 – mgy1
Divide each term by Volume to get
P1 – P2 = ½ r v22 – ½ rv12 + rgy2 – rgy1
Bernoulli's Equation
Change in K.E = ½ mv22 – ½ mv12
Change in G.P.E = mgy2 – mgy1
Work = P1 V – P2 V
 P1 V – P2 V = ½ mv22 – ½ mv12 + mgy2 – mgy1
Bernoulli's Equation
P1 – P2 = ½ r v22 – ½ rv12 + rgy2 – rgy1
Move small cross sectional terms to the
________side and large cross sectional
terms to the ________side
P1 + ½ rv12 + rgy1= P2 + ½ r v22 + rgy2
P + ½ rv2
+ rgy = Constant
Bernoulli's Equation
P1 – P2 = ½ r v22 – ½ rv12 + rgy2 – rgy1
Move small cross sectional terms to the
left side and large cross sectional terms to
the right side
P1 + ½ rv12 + rgy1= P2 + ½ r v22 + rgy2
P + ½ rv2
+ rgy = Constant
Bernoulli's Equation
P + ½ rv2
+ rgy = Constant
The sum of the pressure, the kinetic
energy per unit volume and the potential
energy per unit volume has the
________value at all points along a
streamline
Bernoulli's Equation
P + ½ rv2
+ rgy = Constant
The sum of the pressure, the kinetic
energy per unit volume and the potential
energy per unit volume has the same
value at all points along a streamline
Bernoulli's Equation
P1 + ½ rv12
+ rgy1=
P2 + ½ r v22 + rgy2
________ pipe
P1 + ½ rv12 = P2 + ½ r v22
Swiftly moving fluids exert _____ pressure
than do slowly moving fluids
Bernoulli's Equation
P1 + ½ rv12
+ rgy1=
P2 + ½ r v22 + rgy2
Level pipe
P1 + ½ rv12 = P2 + ½ r v22
Swiftly moving fluids exert less pressure than do
slowly moving fluids
Bernoulli's Equation
P1 + ½ rv12
+ rgy1=
P2 + ½ r v22 + rgy2
Level pipe
P1 + ½ rv12 = P2 + ½ r v22
Swiftly moving fluids exert less pressure than do
slowly moving fluids
labs
 Physics Terms
 Walking speed Walking Velocity
 Graphical Analysis
Slope analysis of position as a function of time graph =
speed /velocity
Slope analysis of velocity as a function of time graph
=acceleration
Area analysis of velocity as a function of time
= displacement
labs



Physics Terms
Walking speed Walking Velocity
Graphical Analysis



Slope analysis of position as a function of time
graph = speed /velocity
Slope analysis of velocity as a function of time
graph =acceleration
Area analysis of velocity as a function of time
= displacement
labs



Physics Terms
Walking speed Walking Velocity
Graphical Analysis



Slope analysis of position as a function of time
graph = speed /velocity
Slope analysis of velocity as a function of time
graph =acceleration
Area analysis of velocity as a function of time
= displacement
labs



Physics Terms
Walking speed Walking Velocity
Graphical Analysis



Slope analysis of position as a function of time
graph = speed /velocity
Slope analysis of velocity as a function of time
graph =acceleration
Area analysis of velocity as a function of time
= displacement
labs



Physics Terms
Walking speed Walking Velocity
Graphical Analysis



Slope analysis of position as a function of time
graph = speed /velocity
Slope analysis of velocity as a function of time
graph =acceleration
Area analysis of velocity as a function of time
= displacement
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions



Physics Terms
Walking speed Walking Velocity
Graphical Analysis









Slope analysis of position as a function of time graph
Slope analysis of velocity as a function of time graph
Area analysis of velocity as a function of time graph
Analysis of a Vertical Jump
Kinematics Equation analysis of cart up and down incline
a=v-vo
t
v =v +vo v= vo + at x=xo+vot+ 1/2 at2
2
Free fall picket fence lab
y vs t graph, vy vs t graph, and g vs t graph
v2 =vo2+2aDx
Labs – kinematics in 1 and 2 dimensions

Horizontally fired projectile



Horizontal range as a function of angle for ground to ground fired
projectiles








Time of flight is independent of horizontal velocity
Time of flight is dependent on height fired from
vox=vocosf
v ox= vx
voy = vosin f
vy = voy + gt
X and Y position as a function of time for a projectile fired at angle
above or below the horizon
X and Y position at maximum height for a projectile fired at an angle
above the horizon
ground to cliff fired projectiles
cliff to ground fired projectiles

Quadratic equation to find time of flight y=yo + voyt + ½ gt2
Labs – kinematics in 1 and 2 dimensions

Horizontally fired projectile



Horizontal range as a function of angle for ground to ground fired
projectiles








Time of flight is independent of horizontal velocity
Time of flight is dependent on height fired from
vox=vocosf
v ox= vx
voy = vosin f
vy = voy + gt
X and Y position as a function of time for a projectile fired at angle
above or below the horizon
X and Y position at maximum height for a projectile fired at an angle
above the horizon
ground to cliff fired projectiles
cliff to ground fired projectiles

Quadratic equation to find time of flight y=yo + voyt + ½ gt2
Labs – kinematics in 1 and 2 dimensions

Horizontally fired projectile



Horizontal range as a function of angle for ground to ground fired
projectiles








Time of flight is independent of horizontal velocity
Time of flight is dependent on height fired from
vox=vocosf
v ox= vx
voy = vosin f
vy = voy + gt
X and Y position as a function of time for a projectile fired at angle
above or below the horizon
X and Y position at maximum height for a projectile fired at an angle
above the horizon
ground to cliff fired projectiles
cliff to ground fired projectiles

Quadratic equation to find time of flight y=yo + voyt + ½ gt2
Labs – kinematics in 1 and 2 dimensions

Horizontally fired projectile



Horizontal range as a function of angle for ground to ground fired
projectiles








Time of flight is independent of horizontal velocity
Time of flight is dependent on height fired from
vox=vocosf
v ox= vx
voy = vosin f
vy = voy + gt
X and Y position as a function of time for a projectile fired at angle
above or below the horizon
X and Y position at maximum height for a projectile fired at an angle
above the horizon
ground to cliff fired projectiles
cliff to ground fired projectiles

Quadratic equation to find time of flight y=yo + voyt + ½ gt2
Labs – kinematics in 1 and 2 dimensions

Horizontally fired projectile



Horizontal range as a function of angle for ground to ground fired
projectiles








Time of flight is independent of horizontal velocity
Time of flight is dependent on height fired from
vox=vocosf
v ox= vx
voy = vosin f
vy = voy + gt
X and Y position as a function of time for a projectile fired at angle
above or below the horizon
X and Y position at maximum height for a projectile fired at an angle
above the horizon
ground to cliff fired projectiles
cliff to ground fired projectiles

Quadratic equation to find time of flight y=yo + voyt + ½ gt2
Labs – kinematics in 1 and 2 dimensions

Horizontally fired projectile



Horizontal range as a function of angle for ground to ground fired
projectiles








Time of flight is independent of horizontal velocity
Time of flight is dependent on height fired from
vox=vocosf
v ox= vx
voy = vosin f
vy = voy + gt
X and Y position as a function of time for a projectile fired at angle
above or below the horizon
X and Y position at maximum height for a projectile fired at an angle
above the horizon
ground to cliff fired projectiles
cliff to ground fired projectiles

Quadratic equation to find time of flight y=yo + voyt + ½ gt2
Labs – kinematics in 1 and 2 dimensions

Horizontally fired projectile



Horizontal range as a function of angle for ground to ground fired
projectiles








Time of flight is independent of horizontal velocity
Time of flight is dependent on height fired from
vox=vocosf
v ox= vx
voy = vosin f
vy = voy + gt
X and Y position as a function of time for a projectile fired at angle
above or below the horizon
X and Y position at maximum height for a projectile fired at an angle
above the horizon
ground to cliff fired projectiles
cliff to ground fired projectiles

Quadratic equation to find time of flight y=yo + voyt + ½ gt2
Labs – kinematics in 1 and 2 dimensions

Horizontally fired projectile



Horizontal range as a function of angle for ground to ground fired
projectiles








Time of flight is independent of horizontal velocity
Time of flight is dependent on height fired from
vox=vocosf
v ox= vx
voy = vosin f
vy = voy + gt
X and Y position as a function of time for a projectile fired at angle
above or below the horizon
X and Y position at maximum height for a projectile fired at an angle
above the horizon
ground to cliff fired projectiles
cliff to ground fired projectiles

Quadratic equation to find time of flight y=yo + voyt + ½ gt2
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - force

Force Table –


Graphical Method – tip to tail sketches
Analytical Method –








Draw vectors from original
Determine angles with respect to x axis
Determine x components
Determine y components
Determine sum of x components
Determine sum of y components
Use Pythagorean Theorem to determine Resultant Force
Use inv tan of sum of y components divided by sum of x
components to determine angle with respect to x axis
Labs - Force



Fan Cart F=ma
Frictionless Cart pulled by falling mass
fromula=a= mfg
(mf+mc)
Friction Block pulled by falling mass
formula = a = mfg – mmg
( mf + mb)
Labs - Force



Fan Cart F=ma
Frictionless Cart pulled by falling mass
fromula= a= mfg
(mf+mc)
Friction Block pulled by falling mass
formula = a = mfg – mmg
( mf + mb)
Labs - Force



Fan Cart F=ma
Frictionless Cart pulled by falling mass
fromula= a= mfg
(mf+mc)
Friction Block pulled by falling mass
formula = a = mfg – mmbg
( mf + mb)
Labs - Force

Frictionless Cart on incline


Friction Block on incline


Formula: a = gsinf
Formula: a = g sinf – mg cos f
Friction Block on incline falling mass


Formula a = mfg - mbg cos f - m mbg sinf
( m f + m b)
Labs - Force

Frictionless Cart on incline


Friction Block on incline


Formula: a = gsinf
Formula: a = g sinf – mg cos f
Friction Block on incline falling mass


Formula a = mfg - mbg cos f - m mbg sinf
( m f + m b)
Labs - Force

Frictionless Cart on incline


Friction Block on incline


Formula: a = gsinf
Formula: a = g sinf – mg cos f
Friction Block on incline falling mass


Formula a = mfg - mbg cos f - m mbg sinf
( m f + m b)
Labs - Force

Frictionless Cart on incline


Friction Block on incline


Formula: a = gsinf
Formula: a = g sinf – mg cos f
Friction Block on incline falling mass


Formula a = mfg - mbg sin f - m mbg cosf
( m f + m b)
Labs - Force









Elevator lab – stationary, accelerating up, constant velocity up,
decelerating up, stationary, accelerating down, constant
velocity down, decelerating down, stationary, free fall
Stationary, Constant Up, Constant Down
Formula: FN = Fg
Accelerating up or Decelerating Down
Formula: FN = Fg + Fnet
Accelerating down or Decelerating Up
Formula: FN = Fg - Fnet
Freefall
Formula: FN=0
Labs - Force









Elevator lab – stationary, accelerating up, constant velocity up,
decelerating up, stationary, accelerating down, constant
velocity down, decelerating down, stationary, free fall
Stationary, Constant Up, Constant Down
Formula: FN = Fg
Accelerating up or Decelerating Down
Formula: FN = Fg + Fnet
Accelerating down or Decelerating Up
Formula: FN = Fg - Fnet
Freefall
Formula: FN=0
Labs - Force









Elevator lab – stationary, accelerating up, constant velocity up,
decelerating up, stationary, accelerating down, constant
velocity down, decelerating down, stationary, free fall
Stationary, Constant Up, Constant Down
Formula: FN = Fg
Accelerating up or Decelerating Down
Formula: FN = Fg + Fnet
Accelerating down or Decelerating Up
Formula: FN = Fg - Fnet
Freefall
Formula: FN=0
Labs - Force









Elevator lab – stationary, accelerating up, constant velocity up,
decelerating up, stationary, accelerating down, constant
velocity down, decelerating down, stationary, free fall
Stationary, Constant Up, Constant Down
Formula: FN = Fg
Accelerating up or Decelerating Down
Formula: FN = Fg + Fnet
Accelerating down or Decelerating Up
Formula: FN = Fg - Fnet
Freefall
Formula: FN=0
Labs - Force









Elevator lab – stationary, accelerating up, constant velocity up,
decelerating up, stationary, accelerating down, constant
velocity down, decelerating down, stationary, free fall
Stationary, Constant Up, Constant Down
Formula: FN = Fg
Accelerating up or Decelerating Down
Formula: FN = Fg + Fnet
Accelerating down or Decelerating Up
Formula: FN = Fg - Fnet
Freefall
Formula: FN=0
Concept Maps
Newtons three laws

Law of inertia



Mass is a measure of inertia
Object at rest stay at rest until net force acts
on them
Objects in with a constant speed moving in a
straight line remain in this state until a net
force acts on them
Concept Maps
Newtons three laws

Law of inertia



Mass is a measure of inertia
Object at rest stay at rest until net force acts
on them
Objects in with a constant speed moving in a
straight line remain in this state until a net
force acts on them
Concept Maps
Newtons three laws

Law of inertia



Mass is a measure of inertia
Object at rest stay at rest until net force acts
on them
Objects in with a constant speed moving in a
straight line remain in this state until a net
force acts on them
Concept Maps
Newtons three laws

Law of inertia



Mass is a measure of inertia
Object at rest stay at rest until net force acts
on them
Objects in with a constant speed moving in a
straight line remain in this state until a net
force acts on them
Force concept maps



Quantitative Second Law
Force is equal to the change in momentum per unit
of time
Force is equal to the product of mass and
acceleration
Force concept maps



Quantitative Second Law
Force is equal to the change in momentum per unit
of time
Force is equal to the product of mass and
acceleration
Force concept maps



Quantitative Second Law
Force is equal to the change in momentum per unit
of time
Force is equal to the product of mass and
acceleration
Force concept maps



Quantitative Second Law
Force is equal to the change in momentum per unit
of time
Force is equal to the product of mass and
acceleration
Force concept maps



Quantitative Second Law
Force is equal to the change in momentum per unit
of time
Force is equal to the product of mass and
acceleration
Force concept maps

Action Reaction Third Law




Equal magnitude forces
Acting in opposite directions
Acting on two objects
Acting with the same type of force
Force concept maps

Action Reaction Third Law




Equal magnitude forces
Acting in opposite directions
Acting on two objects
Acting with the same type of force
Force concept maps

Action Reaction Third Law




Equal magnitude forces
Acting in opposite directions
Acting on two objects
Acting with the same type of force
Force concept maps

Action Reaction Third Law




Equal magnitude forces
Acting in opposite directions
Acting on two objects
Acting with the same type of force
Force concept maps

Action Reaction Third Law




Equal magnitude forces
Acting in opposite directions
Acting on two objects
Acting with the same type of force
Force concept maps

Non contact forces



Force due to gravity
Electrostatic and Magnostatic forces
Strong and Weak nuclear force
Force concept maps

Non contact forces



Force due to gravity
Electrostatic and Magnostatic forces
Strong and Weak nuclear force
Force concept maps

Contact forces



Push – Normal Force – Perpendicular to
a surface
Friction – requires normal force –
opposes motion
Pull – Tension – acts in both directions
Force concept maps

Contact forces



Push – Normal Force – Perpendicular to
a surface
Friction – requires normal force –
opposes motion
Pull – Tension – acts in both directions
Force concept maps

Contact forces



Push – Normal Force – Perpendicular to
a surface
Friction – requires normal force –
opposes motion
Pull – Tension – acts in both directions
Force concept maps

Contact forces



Push – Normal Force – Perpendicular to
a surface
Friction – requires normal force –
opposes motion
Pull – Tension – acts in both directions
Force concept maps

Contact forces



Push – Normal Force – Perpendicular to
a surface
Friction – requires normal force –
opposes motion
Pull – Tension – acts in both directions
Force concept maps

Contact forces



Push – Normal Force – Perpendicular to
a surface
Friction – requires normal force –
opposes motion
Pull – Tension – acts in both directions
Force concept maps

Contact forces



Push – Normal Force – Perpendicular to
a surface
Friction – requires normal force –
opposes motion
Pull – Tension – acts in both directions
Free body diagrams




Fg = force due to gravity = weight
FN = perpendicular push
Ffr = opposes motion
FT = pull = tension
Free body diagrams




Fg = force due to gravity = weight
FN = perpendicular push
Ffr = opposes motion
FT = pull = tension
Free body diagrams




Fg = force due to gravity = weight
FN = perpendicular push
Ffr = opposes motion
FT = pull = tension
Free body diagrams




Fg = force due to gravity = weight
FN = perpendicular push
Ffr = opposes motion
FT = pull = tension
Free body diagrams




Fg = force due to gravity = weight
FN = perpendicular push
Ffr = opposes motion
FT = pull = tension
Labs – Uniform Circular Motion




Swing ride – Tension creates a center seeking force –
centripetal force
Gravitron- Normal force creates a center seeking force –
centripetal force
Hotwheel rollercoaster – Weightlessness at top – gravity
creates the center seeking force – centripetal force
Turntable ride – friction creates a central seeking force –
centripetal force
Labs – Uniform Circular Motion




Swing ride – Tension creates a center seeking force –
centripetal force
Gravitron- Normal force creates a center seeking force –
centripetal force
Hotwheel rollercoaster – Weightlessness at top – gravity
creates the center seeking force – centripetal force
Turntable ride – friction creates a central seeking force –
centripetal force
Labs – Uniform Circular Motion




Swing ride – Tension creates a center seeking force –
centripetal force
Gravitron- Normal force creates a center seeking force –
centripetal force
Hotwheel rollercoaster – Weightlessness at top – gravity
creates the center seeking force – centripetal force
Turntable ride – friction creates a central seeking force –
centripetal force
Labs – Uniform Circular Motion




Swing ride – Tension creates a center seeking force –
centripetal force
Gravitron- Normal force creates a center seeking force –
centripetal force
Hotwheel rollercoaster – Weightlessness at top – gravity
creates the center seeking force – centripetal force
Turntable ride – friction creates a central seeking force –
centripetal force
Labs – Uniform Circular Motion




Swing ride – Tension creates a center seeking force –
centripetal force
Gravitron- Normal force creates a center seeking force –
centripetal force
Hotwheel rollercoaster – Weightlessness at top – gravity
creates the center seeking force – centripetal force
Turntable ride – friction creates a central seeking force –
centripetal force
Labs – Uniform Circular Motion




Swing ride – Tension creates a center seeking force –
centripetal force
Gravitron- Normal force creates a center seeking force –
centripetal force
Hotwheel rollercoaster – Weightlessness at top – gravity
creates the center seeking force – centripetal force
Turntable ride – friction creates a central seeking force –
centripetal force
Labs – Uniform Circular Motion



Cavendish Torsion Balance – Fg = G m1m2
r2
Universal Gravitational Constant – big G = 6.67x10-11 Nm2/kg2
Mass of the earth calculation mg = G m1me
r2
Earth’s moon orbital velocity calculation
Satellite orbital velocity calculation
Geostationary Satellite orbital velocity and orbital radius calculation
Bipolar Star calculation
Fc = mv2 = G m1m2 = Fg
r
r2
v= 2pr(rev)
t
Labs – Uniform Circular Motion



Cavendish Torsion Balance – Fg = G m1m2
r2
Universal Gravitational Constant – big G = 6.67x10-11 Nm2/kg2
Mass of the earth calculation mg = G m1me
r2
Earth’s moon orbital velocity calculation
Satellite orbital velocity calculation
Geostationary Satellite orbital velocity and orbital radius calculation
Bipolar Star calculation
Fc = mv2 = G m1m2 = Fg
r
r2
v= 2pr(rev)
t
Labs – Uniform Circular Motion



Cavendish Torsion Balance – Fg = G m1m2
r2
Universal Gravitational Constant – big G = 6.67x10-11 Nm2/kg2
Mass of the earth calculation mg = G m1me
r2
Earth’s moon orbital velocity calculation
Satellite orbital velocity calculation
Geostationary Satellite orbital velocity and orbital radius calculation
Bipolar Star calculation
Fc = mv2 = G m1m2 = Fg
r
r2
v= 2pr(rev)
t
Labs – Uniform Circular Motion



Cavendish Torsion Balance – Fg = G m1m2
r2
Universal Gravitational Constant – big G = 6.67x10-11 Nm2/kg2
Mass of the earth calculation mg = G m1me
r2
Earth’s moon orbital velocity calculation
Satellite orbital velocity calculation
Geostationary Satellite orbital velocity and orbital radius calculation
Bipolar Star calculation
Fc = mv2 = G m1m2 = Fg
r
r2
v= 2pr(rev)
t
Labs – Uniform Circular Motion



Cavendish Torsion Balance – Fg = G m1m2
r2
Universal Gravitational Constant – big G = 6.67x10-11 Nm2/kg2
Mass of the earth calculation mg = G m1me
r2
Earth’s moon orbital velocity calculation
Satellite orbital velocity calculation
Geostationary Satellite orbital velocity and orbital radius calculation
Bipolar Star calculation
Fc = mv2 = G m1m2 = Fg
r
r2
v= 2pr(rev)
t
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
acceleration
Mass
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum (Change)
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum (Change)
Force
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum
Force
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum
Force
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum
Force
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum
Force
Work /
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum
Force
Work / Energy
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum
Force
Work / Energy
Kinematics / Dynamics Relationships

Distance / Displacement

Speed/Velocity
Time
Mass
acceleration
Momentum
Force
Work / Energy
Power
Kinematics / Dynamics
Relationships

Distance/Displacement


m/s
Time
Mass
Kinematics / Dynamics
Relationships


Distance/Displacement
Speed/Velocity=m/s


m/s/s=m/s2
Time
Mass
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Speed/Velocity = m/s
Acceleration =m/s2
Mass
Kinematics / Dynamics
Relationships

Distance/Displacement
Time
Mass
Speed/Velocity=m/s
kg m/s
Acceleration= m/s2
Kinematics / Dynamics
Relationships

Distance/Displacement
Time
Mass
Speed/Velocity=m/s
kg m/s -momentum
Acceleration= m/s2
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2




kg m/s/s=kg m/s2
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2




Force=Newton=kg m/s2
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2


kg m/s2
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2



Force=Newton =kg m/s2
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2
Force= Newtons=kg m/s2






N m = Kg m/s2 m
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2
Force=Newtons = kg m/s2






N m = Kg m2/s2
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2
Force=Newton=kg m/s2



Work /
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2



Force=Newton=kg m/s2
Work / Energy = Joule = N m = kg m2/s2
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2
Force=N=kg m/s2

Work / Energy=J = N m = kg m2 / s2




kg m2/s2/s
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2
Force=N=kg m/s2

Work / Energy=J = N m = kg m2 / s2




kg m2/s2/s = kg m2/s3
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2
Force=N=kg m/s2

Work / Energy=J = N m = kg m2 / s2




kg m2/s2/s = kg m2/s3 = N m = J
s
s
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2
Force=N=kg m/s2

Work / Energy=J = N m = kg m2 / s2




kg m2/s2/s = kg m2/s3 = N m = J = W
s
s
Kinematics / Dynamics
Relationships


Distance/Displacement
Time
Mass
Speed/Velocity=m/s
Momentum=kg m/s
Acceleration=m/s2
Force=N=kg m/s2

Work / Energy=J = N m = kg m2 / s2




Power
kg m2/s2/s = kg m2/s3 = N m = J = W
s
s
Graphical Analysis


Position
Time
Graphical Analysis


Position
Time
Graphical Analysis


Position
Time
stopped


Position
Time
Graphical Analysis


Position
Time
Constant velocity –constant momentum –
no acceleration


Position
Time
Graphical Analysis


Position
Time
Constant velocity – constant momentum –
no acceleration


Position
Time
Graphical Analysis


Position
Time
Increasing velocity – increasing momentum
- accelerating


Position
Time
Graphical Analysis


Position
Time
Increasing velocity – increasing
momentum - accelerating


Position
Time
Graphical Analysis


Position
Time
Decreasing velocity – decreasing
momentum - decelerating


Position
Time
Graphical Analysis

Position


Time
Decreasing velocity – decreasing
momentum - decelerating

Position


Time
Graphical Analysis

O m/s
Velocity vs Time

Velocity

0 m/s

time

O m/s
Stopped

O m/s

O m/s
Accelerating

O m/s

O m/s
accelerating

O m/s
decelerating

O m/s
decelerating

O m/s
decelerating

O m/s
decelerating

O m/s

O m/s
Constant velocity

O m/s

O m/s
Constant Velocity

O m/s
Graphical Analysis Slopes

Postion

time
Slope = velocity

Postion

time
Velocity vs Time Slope

Velocity

time
Slope of V vs T = Acceleration

Velocity

time
Area of V vs T = ?

Velocity


time
Area of V vs T = Distance traveled


Velocity
time
Area of V vs T = Distance traveled


Velocity
time
Force vs Distance

Force
Distance
Force vs Distance


Force
slope =
spring constant
K=N
m



Distance
Force vs Distance

Force

E.P.E=1/2 Kx2


Distance
Force vs Distance

Force


Area = Work


Distance
Force vs time


Force
Time
Force vs time Area


Force
Change in Momentum =
Time
Force vs time Area




Force
Change in Momentum = D p = J
Impulse = Average Force * time
J = Favg t = N*s
Time