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Phys 220 Review
Part 1
Newton's First Law
If the total force acting on an object is zero, the
object will maintain its velocity (magnitude and
direction) forever.


Inertia is a measure of an object's resistance to
change in motion – depends on mass.
Mass is a measure of how much matter an
object contains. An intrinsic property.
Newton's Second Law


Many different forces can be acting on an object
simultaneously.
The effect of all these forces is the same as the
effect of one force with the same magnitude and
direction as the sum of all the forces.

Ftot =

F
The acceleration of an
object is related to the
net force and the mass

of
F = ma
the object.
Units of Force:
1newton N = 1kg m / s 2
Newton's Third Law


When on object exerts a
force on a second object,
the second object exerts a
force of the same
magnitude and opposite
direction on the first object.
The action – reaction
principle.
Constant Acceleration
Normal Force


Perpendicular (“normal”) to the plane of
contact.
Intuitively, a force of support (e.g. standing
on the floor, holding a weight in your
hand).
Kinetic Friction
A moving object can
experience kinetic
friction.

Ffriction = μk N
The coefficient of
kinetic friction is a
pure number and its
value depends on
the surfaces
involved.
Static Friction
A stationary object can
experience static friction
(there is no slipping between
the surfaces).
The magnitude of the friction
force depends on the push
(up to a certain magnitude).

Ffriction
μs N
This force allows walking and rolling
Tension


Strings (ropes, cables,
etc.) exert forces on the
objects they are
connected to.
This force is due to the
tension of the string.
Pulleys

Can be used to redirect forces.

Can be used to amplify forces.
Newton’s 1st Law in 2D
For an object at constant velocity, forces
must sum to zero

F 0
Equation for each direction,
Fx
0
Fy
0
Statics
(Translational) Equilibrium – velocity and
acceleration are 0.
Applies to many, practical cases: bridges,
buildings, …

F=0
(in 2-D)
(in translational equilibrium)
(in 3-D)
Fx = 0
Fx = 0
Fy = 0
Fy = 0
Fz = 0
Projectile Motion
Things flying through the air
under the force of gravity.
Now something slightly harder:
Something moving horizontally
y
x
y
y0
x vt
1 2
gt
2
Reference Frames
Newton’s Laws gives consistent
results when applied from any
reference frame moving at
constant velocity.
Uniform Circular Motion
Circular motion with a
constant speed
Since direction is
always changing, so is
velocity
Velocity vector is
tangent to the circle
Basic Properties
Properties can be derived by basic definitions
The period, T (time it takes to complete one
rotation), is:
2 πr
T=
v
For objects taking the same
time to complete a circuit,
the velocity of the object at greatest
radius is the greatest.
Centripetal Acceleration
Velocity is always changing direction so the
object is accelerating.
2
v
ac =
r
Forces on Objects with Circular
Motion
An object moving in a circle must have acceleration
of ac.
There must be a force(s) to provide this
acceleration.


Examples:
F = m ac
– Spinning a rock on a string
– Car on a curve
– Roller coaster loop
– Orbits of celestial bodies
Example: Vertical Circle
Non-uniform circular motion
 mv 2
F=
= Tbottom
r
 mv 2
F=
= mg
r
mg
 mv 2
F=
= Ttop + mg
r
 mv 2
F=
=N
r
mg
N
Newton's Law of Gravitation
Acts on both masses
involved
Distance between the
centers of the objects
Always attractive
Acts along the line
connecting the centers
of the objects.
Fgrav =
Gm1m2
r2
G M Earth
g=
2
r Earth
Work
The “scalar product” (dot product) of force and
displacement is work.
“Scalar product” means we are only concerned
with the component of force along the direction
of displacement.

W=F

r
 
F r cosθ
SCALAR
Units:
N m = J Joule
Kinetic Energy
Rearrange definition of work and Newton's 2nd
law and we get 1 2 1 2
W = mv f
mvi
2
2
We call these kinetic energy because it has units
of energy (Joules) and is related to the motion
of the object (by v).
Potential Energy
Whether an object of mass m is
dropped straight down a height h
or slid down an incline through a
height h, the work done by the
Earth on the object is mgh.
Any object near the earth's surface
has a potential energy associated
with its height.
This is an energy stored in the system
(the Earth and the object).
Elastic Potential Energy
Hooke's Law
Fspring = kx
Negative because it opposes
displacement
1 2
PE spring = kx
2
Conservation of Energy
KEi+ PEi + W = KE f + PE f
Non-conservative forces convert mechanical
energy (PE and ME) to heat.
The energy is not lost!
An external agent can add energy to the system
by doing work on the system but energy is
taken from the agent (because the system
does the opposite work on the agent).
The total energy in the universe is conserved
Collisions and momentum
F2->1
1
vi
vf
1
1
2
2
2
F1->2
Vf
Force present for short period of time. Hard to
predict. But we know F1->2 + F2->1 = 0.
Collision
1
vi
vf
1
m1
2
2
m2

p 0
Vf


p mv
Constraint on the momentum. Forces don’t appear
Momentum
Some objects can be described as
point particles
Some objects need to be considered
as a collection of particles.

ptot =

pi =

mi vi


p= mv
Center of Mass
Center of mass allows us to predict the motion
of an extended body (made of many point
particles).
x cm =
y cm =
∑ i mi x i
∑ i mi
∑ i mi y i
∑ i mi
=
=
∑ i mi x i
M tot
∑ i mi y i
M tot
Torque
Rotational equivalent of force –
torque.
Related to force applied,
distance from the pivot, and
the angle between the radial
direction and the force
Rotational Inertia
F = ma
τ = Iα
A constant for each
object. Can be
calculated
Complete Analogy
We can make substitutions into all of the equations we have
seen so far to get the rotational equivalent (Newton's Second
Law, constant acceleration equations, Equilibrium condition,
etc.)
Combined Linear and Rotational Motion
A weight is attached to a massive frictionless pulley. What is its
acceleration when dropped?
forces on mass
T

F

mwa
mw g
mw a
1
m p a mw g mwa
2
mw g
a
1
m p mw
2
r
torques on pulley
mp
I
Tr
T
mw
mw g
Tr
a/r
1
2
I
mp r
2
12 a
1
T mp r mpa
2
2 r
Rotational Motion
Rotational Analogy applies to equilibrium
Also applies to dynamics analysis