Download Topic 1: Math and Measurement Review

Topic 1: Math and Measurement Review
I- Significant Figures
A- The digits of a measured value that are known with certainty (only used with units)
B- Determining the Number of Significant Figures:
1- Non zero digits are always significant
2- Zeroes may or may not be significant depending on their position:
a- Zeroes that appear before a non zero digit are not significant
Example: 0.002m = 1 Sig Fig, 0.13m = 2 Sig Figs
b- Zeroes that appear between non zero digits are significant
Example: 0.705g = 3 Sig Figs, 2006 = 4 Sig Figs
c- Zeroes that appear after a non zero digit are significant only if:
i- Followed by a decimal point
Example: 40sec = 1 Sig Fig, 40.sec = 2 Sig Figs
ii- They appear to the right of the decimal point
Example: 37.0g = 3 Sig Figs, 4.100m = 4 Sig Figs
II- Scientific Notation
A- A way of writing numbers to a power of 10
III- Geometry of a Triangle
A- Right Triangles
Pythagorean Theorem
B-Other Triangles
Law of Cosines- used when you are given 2 sides and the angle
between them and need to find the third side
Law of Sines- used when you are given 2 angles and a side and
you need to find the second side
IV- The Metric System
A- Metric System Facts
1- Used in everyday life by almost every country (not the United States)
2- System is based on powers of 10
3- Used worldwide by the scientific community
B- Fundamental (Base) Units- set of units on which a system of metric is based
1- Meter (m)- unit of length
a- Doorknob = 1 meter
b- Width of a door = 1 meter
c- Height of a person = 1.5 meters
d- 1 meter is approximately 39 inches
e- Defined as the distance light travels in
second in a
2-
34-
5-
vacuum
Kilogram (kg)- unit of mass
a- Amount of matter in an object
b- Approximate weight of 2.2 pounds on Earth
c- Mass of a student = 50-60 kg
d- Standard is a platinum iridium cylinder that is kept at constant temperature
and humidity in a dustless vault
Second (s, sec)- unit of time
a- Standard based upon the frequency of vibrations of cesium-133 atom
Kelvin (K)- unit of temperature
a- Standard is based on the point at which solid, liquid, and gaseous water
coexist simultaneously (273.16 K)
Mole (mol)- unit of number of particles
a- Standard is based on the number of atoms contained in 0.012kg of
Carbon-12 (
atoms)
6- Candela (cd)- unit of luminous intensity
7- Ampere (amp)- unit of electric current
C- Derived Units
1- Units that are based on the fundamental units
D- Order of Magnitude
1- Power of 10 closest to its value
2- Allows you to compare and estimate a measure
E- Prefixes
1- Changes the value of a unit by powers of 10
2- King Henry Drank Uncle Dave’s Chocolate Milk
Kilo-Hecto-Deka-Unit-Deci-Centi-Milli
1000 100 10
0.1 0.01 0.001
V- Estimations
A- Mass of a student = 65 kg
B- Height of a student = 1.5m
C- Height of a doorknob = 1m
D- Mass of a nickel = 5g
E- Mass of an egg = 50g
F- 1 kg = 2.2 pounds
Topic 2: Motion
I- Constant Motion
A- Vocabulary
1- Distance- the total length traveled by the object
a- Does not depend upon the direction traveled by the object
b- Measured in meters or kilometers
2- Displacement- the total length between the starting point and the ending point
a- Depends on the direction traveled by the object
b- Measured in meters or kilometers
3- Speed- how fast an object travels (distance covered per unit of time)
a- Does not depend on the direction traveled by the object
b- Measured in meters per second or kilometers per hour (convert km/hr to
m/s by multiplying by 1000 and then dividing by 3600)
4- Velocity- how fast an object travels in a particular direction (displacement per
unit of time)
a- Depends on the direction traveled by the object
b- Measured in m/s or km/hr
B- Constant Motion
1- Any type of motion that does not change over a period of time
2- The distance/displacement covered by the object each unit of time remains the
same
3- Distance/Displacement vs. Time Graph
Direct proportion
d
t
Delta symbol is dropped because
the graph goes through the origin
4- The slope of a distance vs. time graph is the average speed of the object
5- The slope of a displacement vs. time graph is the average velocity of the
object
II- Acceleration
A- Acceleration- any change in velocity (speed or direction) over a period of time
1- An object can accelerate if it:
a- Speeds up
b- Slows down
c- Turns (centripetal acceleration)
2- Acceleration will be constant the entire problem
3- The change in velocity (up or down) will remain the same for the entire
problem
B- How do we know when an object is speeding up or slowing down?
1- If velocity and acceleration have the same sign, the object is speeding up
(either both + or both -)
2- If velocity and acceleration have opposite signs, the object is slowing down
(one +, one -)
C- Graphs
Distance vs. Time
Velocity vs. Time
The slope of a
velocity-time
graph is the
acceleration of
the object
D- Equations
I- Free Fall
A- Vocabulary
1- Free Fall- the motion of an object under the influence of gravity only
a- Air resistance is always neglected
b- A type of accelerated motion in the vertical direction (accelerated motion)
 velocity changes every second of travel
2- Acceleration due to Gravity
a- The same for all objects when air resistance is neglected
b- Does not depend on size or mass
i- An elephant accelerates at the same rate as a feather, but they appear to
accelerate at different rates due to air resistance
c- On or near the surface of the Earth, acceleration due to gravity is
9.81
directed downward
i- Therefore,
anytime an object travels vertically
B- Scenario 1- Object Dropped
1- When an object is dropped, the following are always true on or near the
Earth’s surface:
because the object starts from rest
because the object us being accelerated by gravity
*will not be stated in the problem- remember!
C- Scenario 2- Object is thrown straight up
1- When an object is thrown straight up and caught at the same point, the
following are always true:
a- On the way up…
iVelocity is positive and acceleration is negative, therefore the
object slows down
b- On the way down…
iVelocity is negative and acceleration is negative, therefore the
object speeds up
c- At the top
Velocity = 0m/s
d- Since acceleration on the way up is the same as the acceleration on the
way down:
iThe distance traveled up is the distance traveled down
iiThe time to travel up is the time to travel down
iiiThe speed with which the object is released is the speed with
which the object is caught
ivVelocity will NOT be the same: on the way up velocity is positive,
on the way down velocity is negative
III- Graphical Analysis
A- Remember:
1- The sign (+/-) of a value in physics indicates the direction
a- The right or up is positive
b- The left or down is negative
B- Slope
1- Slope of a straight line is constant
a- Therefore, the quantity that the slope represents is constant
2- Slope of a curve is not constant
a- Therefore, the quantity that the slope represents is not constant
C- What does the slope represent?
a- Distance vs. Time- average speed
b- Displacement vs. Time- average velocity
c- Velocity vs. Time- acceleration
*Average takes into account constant and changing motion
D- Area under the Graph
a- A shortcut way to find distance or displacement
b- Only when given a speed or velocity vs. time graph
c- Area of a rectangle or square:
or
d- Area of a triangle:
Velocity vs. Time Graph
A
V
AB: object is moving to the right, acceleration = 0, velocity
is constant
B
BC: object is moving right with positive velocity, slowing
down because it has a positive velocity and negative
acceleration
C
T
C: object stops, velocity is 0, changes direction
CD: object is moving to the left, speeding up because it has
negative velocity and negative acceleration
D
E
DE: object is moving to the left, negative velocity,
acceleration is 0, constant velocity
*Acceleration is equal to the slope
Topic 3: Vectors
I- Scalar vs. Vector
A- Scalar- any quantity that represents magnitude only
1- Examples: distance, speed, time, mass, temperature, work, power, energy
B- Vector- any quantity that represents magnitude and direction
1- Examples: displacement, velocity, acceleration, force, momentum, electrical
field, gravitational field, magnetic field
II- Vectors
A- Arrows are drawn to represent the quantity (need arrowheads)
1- Length of the arrow is the magnitude of the vector
2- Choose an appropriate scale
3- Arrowhead represents the direction
B- Vector Composition- combining two or more vectors to get a single vector that
has the same effect as the original vector
C- Resultant- a single vector that has the same effect as two or more vectors
D- Equilibrant- a single vector that balances the resultant
1- Equal in magnitude and opposite in direction to the resultant
III- Types of Vectors
A- Vectors Acting in the Same Direction
1- Example- A student walks 50 km east and then runs 90 km east. What is her
resultant displacement?
a- Graphical Solution
iDraw vectors head to tail (the head of one vector is touching the
tail of another)
iiThe resultant is drawn from the starting point to the head of the last
vector
50 km E
90km E
R = 140 km E
a- Mathematical Solution
iThe magnitude of the resultant is the sum of the individual
magnitudes
iiThe direction remains the same
iii= 0̊
B- Vectors Acting in Opposite Directions
a- Graphical Solution: Head to tail method
R = 40 km W
50 km E
90 km W
b- Mathematical Solution
iThe magnitude of the resultant is the difference between the
individual magnitudes
iiThe direction is the same as the larger vector
iii= 180̊
C- Vectors Acting at Right Angles
a- Graphical Solution: Head to tail method
R = 104 km
at 60̊ N of E
90 km N
60̊
50 km E
b- Mathematical Solution
i- Magnitude:
ii- Direction (angle):
Da-
Vectors Acting in Any Direction
Graphical Solution: Head to tail
R = 136 km at
20̊ N of E
90 km at 30̊
N of E
20̊
50 km E
IV- Concurrent Forces
A- Force- any push or pull (measured in Newtons)
1- A vector quantity- has magnitude and direction
B- Concurrent- acting on the same object (from the same point) at the same time
1- Begin at the same point, breaking the first rule of the head to tail method of
vector composition
2- One vector must be relocated before the resultant is drawn
3- The relocated vector must be the same size and in the same direction
4- The resultant is then drawn from the starting point to the head of the relocated
vector
Relocated
Vector
V- Vector Resolution
A- Vector Resolution- breaking a resultant into its components
B- Components- the vectors that make up a resultant
1- The number of components that any resultant can be broken into is unlimited
2- Horizontal Component:
3- Vertical Component:
Topic 4: Two Dimensional Motion and Trajectories
I- Introduction
A- Types of two dimensional motion
1- Projectiles fired horizontally (a ball rolled off the table and allowed to fall to
the ground)
2- Projectiles fired at an angle (a football kicked)
B- All projectiles follow a parabolic curve
1- Launched horizontally- half the parabola
2- Launched at an angle- the whole parabola
C- Two dimensional motion can be broken up into horizontal and vertical motion
1- The motion of the vertical direction is independent of the motion in the
horizontal direction and vice versa- they don’t affect each other
D- Horizontal Motion
1- Occurs parallel to the ground along the x-axis
2- Whatever direction, make it positive- only travels forward
3- Neglect air resistance
4- Constant motion
5- Velocity remains the same for the entire flight
E- Vertical Motion
1- Occurs perpendicular to the ground along the x-axis
2- Neglect air resistance
3- Accelerated motion (due to gravity)
4- Velocity changes as it moves vertically
II- Projectile Launched Horizontally
A- Velocity:
stays the same the entire problem since
accelerating so it starts at
B- Time:
and then increases at the rate of
depends on the height above the ground (
due to gravity ( ), NOT velocity
C-
does not affect time of flight, only affects
D- If friction were present,
,
(range) would be shorter
is
( )
) and the acceleration
E- The actual path with air resistance has a smaller
, so the parabola is skinnier
III- Projectile Launched at an Angle
A-
,
is constant because
B-
,
decreases to the top, where it is
C-
=
, and then increases
D- Achieve maximum range when it is fired at a 45 degree angle
Topic 5: Newton’s Laws
I- Forces
A- Introduction
1- Kinematics- the study of how objects move
2- Dynamics- the study of why objects move
3- Sir Isaac Newton- English physicist who created three laws of motion to
explain the relationship between motion and what causes it
4- Force- any push or pull
a- Vector quantity (magnitude and direction)
b- Measured in Newtons (N)
B- Contact vs. Non-Contact Forces
1- Contact Forces- one object touches another object
a- Examples- you push down on the chair, the chair pushes up on you; coat
pushes down on hook, hook pushes up on coat
2- Non-Contact Forces- one object acts on another object through a field
a- Examples- the earth pulls objects downward through a gravitational field,
the north pole of a magnet attracts the south pole of another magnet
through a magnetic field
C- Types of Forces
1- Gravitational Force- attractive force that exists between all objects
a- Weakest type of force
b- Holds the moon in its orbit (Earth acting on the moon)
c- Causes tides (moon acting on Earth)
2- Electromagnetic Force- results from a basic property of particles called
electric charge
a- Charged particles (at rest or moving) exert forces on each other
b- Moving charged particles create magnetic fields
c- Very large compared to gravitational force
3- Strong (Nuclear) Force- holds the particles of the nucleus together
a- Strongest of the three forces
b- Approximately 200x stronger than electromagnetic force
c- Acts over distances the size of the nucleus of an atom
II- Equilibrium
A- Equilibrium- a state of balance
1- The net (total) force acting on the object is zero
B- Static Equilibrium- object is at rest
a- Total force acting on the object equals zero (
)
C- Dynamic Equilibrium- object is moving at a constant velocity
a- Total force acting on the object is zero (
)
III- Newton’s first law of motion
A- An object in a state of equilibrium(static or dynamic) will remain in equilibrium
until an unbalanced force acts on it
1- Unbalanced forceB- Inertia
1- Newton explained the first law by creating the word inertia
2- Property f matter that causes an object to resist a change in its motion
3- Directly related to mass (as mass increases, inertia increases)
C- Free Body Diagram
1- Weight ( ) always points straight down
2- Normal force (
) always pushes perpendicular to the surface
3- Tension ( ) always pulls along the line of the string
4- Applied force (
) from a person or other source in any direction
IV- Newton’s Second Law
A- Acceleration- any change of velocity(speed or direction) over a period of timeobject can start moving, increase or decrease in speed, stop moving, or change
direction
B- Second law- An unbalanced force applied to an object will cause the object to
accelerate in the direction of the unbalanced force
1- Unbalanced force  resultant force 
C- When more than one force is acting on the object the total (net) force causes
acceleration
a = acceleration (
)
= Net force (N)
m = mass (kg)
Unit derivation- a Newton is a derived unit(not a fundamental unit)
V- Newton’s Third Law
A- Every action has an equal and opposite reaction
VI- Weight/ Gravitational Force
A- Mass- a measure of the amount of matter in an object
1- Unit = kg
2- Measured on a triple beam balance
3- Mass does not change!
B- Weight/gravitational force- a measure of the gravitational pull of an object
1- The force of attracting between a planet and an object
2- Unit = Newton
3- Measured on a spring scale
C- Weight and the second law
1- Unbalanced force causes an object to accelerate in the direction of the
unbalanced force
a- Unbalanced force  Weight ( )
b- Acceleration  Gravity (g)
(g = acceleration due to gravity)
D- Apparent Weight (
)
1- Feel heavier when
>
(accelerating upward in an elevator)
2- Feel lighter when
<
(accelerating downward in an elevator)
3- Feel normal when
=
(at rest or moving with constant velocity)
4- An elevator could be traveling up or down because:
a- If the elevator is traveling up, v is positive, a is negative, so it is slowing
down
VII-
b- If the elevator is traveling down, v is negative, a is negative, so it is
speeding up
Friction
A- Friction- a force that opposes the motion between surfaces that are in contact with
each other
1- The direction of the force is parallel to the surface and in a direction that
opposes the slipping of the two surfaces
B- Types of friction
1- Static Friction
a- At rest, not moving
b- The force that opposes the start of motion
c- Static friction keeps the object stationary
d- When the magnitude of your force on an object is equal to or greater than
the maximum value of static friction, the object begins to move
2- Kinetic Friction(sliding friction)
a- Kinetic  motion (constant or accelerated)
b- The force that opposes the sliding of one object over another
c- The force of kinetic friction is less than the force of static friction
iIt is easier to keep an object moving than to start it
C- What does the force of friction depend on?
1- The force pushing the surfaces together ( )
2- The coefficient of friction ( )
3- Does NOT depend on surface area!
D- Coefficient of Friction
1- A number that relates the relative strength of friction
2- Depends on the surfaces in contact with each other
3- Has no unit!
E- How do you calculate the force of friction?
1- Static equilibrium along the y-axis:
2- Accelerating along the x-axis:
VIII- Motion on a Frictionless Inclined Plane
A-
always acts downward, perpendicular to the horizontal
BC-
always acts upward, perpendicular to the surface
does not equal
because they do not act in opposite directions ( between
and
D- Motion is always parallel to the inclined plane (either up or down the inclined
plane)
E- Axes are chosen parallel and perpendicular to the inclined plane ┴
1- Always downward, perpendicular to the surface
2because they act along the perpendicular axis and
1- Without friction,
is the only force acting along the axis of motion
2- Trick:
IX- Motion on an Inclined Plane with Friction
A-
always acts downward, perpendicular to the horizontal
B-
always acts upward, perpendicular to the surface
C-
does not equal
because they do not act in opposite directions ( between
and
D- Motion is always parallel to the inclined plane
1- Always downward, perpendicular to the surface
2because they act along the perpendicular axis and
1- Increases as you increase
E- Friction- a force that opposes motion
1- Always acts opposite motion, parallel to the surface
2- Static Friction- opposes the start of motion
a- Maximum value of friction because it is just beginning to
move (
)
b- Kinetic Friction- opposes the motion of one object over
another
a- Moving with constant velocity (
b- On an incline with friction,
and
)
both act along the
parallel axis
Topic 6: Circular Motion and Gravitation
I- Periodic Motion
A- Motion that repeats at regular intervals
1- Example- swinging a toy over your head (uniform circular motion)
II- Uniform Circular Motion
A- Object is moving in a circular path with constant speed
1- Speed = the magnitude of the velocity
B- The magnitude of the velocity is constant but the direction is always changing
C- According to Newton’s second law, an object moving at a constant speed will
continue to move at a constant speed in a straight line until acted upon by an
unbalanced force
D- The velocity vector is always directed in a straight line, tangent to the circular
path
E- Since the object is continuously moving, the direction of the tangent line is not
constant.
F- Any change in velocity (speed or direction) is acceleration
1- Centripetal acceleration- the acceleration experienced by an object in uniform
circular motion due to its continuous change in direction
= centripetal acceleration
= velocity
r = radius
2- According to Newton’s Second Law, acceleration is caused by an unbalanced
force
a- Centripetal Force- the unbalanced force experienced by an object
undergoing uniform circular motion
iii-
According to Newton’s Second Law, the net force and acceleration
have a direct relationship[ and always act in the same direction
In order to maintain a circular path, the object must constantly
accelerate towards the center of the circular path and therefore
is toward the center as well
III- Period/Frequency
A- Period- the time required to make one complete circle (unit = seconds)
B- Frequency- the number of circles completed in one second (unit = Hertz, Hz)
C- Period and frequency are reciprocals:
IV- Calculating the Speed
A- The magnitude of the velocity (speed) of an object undergoing uniform circular
motion is constant
1- The distance traveled in a circle is the circumference (
)
V- The Law of Universal Gravitation
A- Introduction
1- All objects that move in a horizontal circle maintain a constant speed
2- In order to follow a circular path, the direction of the motion must change
constantly and therefore the velocity is changing
3- Any change in velocity requires an unbalanced force which for circular
motion is called centripetal force
a- Where does centripetal force come from?
i-
If a person is running on a track or a car is driving around a turn,
then the unbalanced force ( ) is supplied by friction (
)
ii-
For an object attached to a string and swung in a horizontal circle,
the unbalanced force ( ) is supplied by the tension in the string
(
)
iii-
Where does the unbalanced force come from that is necessary to
keep the planets and other satellites in their orbits? This was
answered by Newton in the Law of Universal Gravitation
B- The Law of Universal Gravitation
1- All objects attract other objects- attraction is universal
2- Attraction between ordinary objects is extremely weak and therefore
undetectable
3- If one or both of the objects contain an enormous amount of mass, the force of
attraction becomes significant
= gravitational force (N)
G = universal gravitation constant
m = mass (kg)
r = distance between the centers of the objects (m)
4- On or near the surface of the earth,
C- Relationships
1- Relationship between
and
: direct relationship

Increase or decrease
OR
, increase or decrease
by the same factor

Increase or decrease
decrease
2- Relationship between
AND
, increase or
by the product of the factors
and : inverse square relationship

Increase , decrease
by the factor squared

Decrease , increase
by the factor squared
VI- Vertical Circles
A- Roller Coaster
1- Top of the Hill
a- Free body Diagram:
going up
b- Forces:
Upward
and
(-)
exerted by the track (or cart)
Downward
c-
(+) going down into the center of the circle,
exerted by Earth
combine following the rules of vector composition to provide
the
d- The
e-
is always directed towards the center of the circle
feel lighter
f- How fast can the coaster go until the rider just barely looses contact with
the seat? Set
2- Bottom of the Valley
a- Free Body Diagram:
circle
b- Forces:
iUpward
ii-
Downward
(-) going down,
(+) going into the center of the
exerted by the track (or cart)
exerted by Earth
c-
and
combine following the rules of vector composition to provide
the
d-
feel heavier
e-
(Greatest
3- Upside-down at the top of a Loop
a- Free Body Diagram: (+) and
the circle
b- Forces:
iBoth
ii-
and
)
(+) going down towards the center of
point toward the center and together supply
This means if the speed is too small,
will be negative and the
rider or cart will fall downward. Therefore, carts have wheels on
both sides of the track
B- Object Swinging on a String ( is always towards the center)
1- Top
a- Both
and
are directed downward towards the center of the circle
2- Bottom
ais going up toward the center of the circle,
is going down
.
3- Side
ais going left or right towards the center of the circle,
is going down
Topic 7: Momentum and Conservation
I- Momentum
A- Inertia of motion (an object will remain in motion until acted upon by an
unbalanced force
B- The product of an object’s mass and velocity
p = momentum (
v = velocity
m = mass (kg)
1- momentum is a vector quantity- same direction as the velocity
II- Impulse
A- Second law- an unbalanced force (
) causes an object to accelerate (change
velocity) and therefore causes a change in momentum
t = time (seconds)
J = impulse (
1- Impulse (the product of net force and time ) is a vector quantity- same
direction as the net force
III- Momentum Impulse Theorem
A- Newton’s second law
a- The amount of change depends on
and t
a- Impulse = change in momentum
B- The impulse
) imparted on an object must equal the change in momentum
(
C- As time decreases,
increases- you need to increase time so you can decrease
IV- Law of Conservation of Momentum
A- When two or more objects interact, momentum can be transferred from one object
to another
B- System- a defined group of objects
1- Closed (isolated) system- no external force acting on it
C- Third law- for every action there is an equal and opposite reaction
1- Example- A baseball exerts a force that is equal and opposite to the net force
the bat exerts on the baseball. The impulse (
will be the same for both
the bat and the baseball. The change in momentum (
) will be the same for
both the bat and baseball. The baseball has a greater change in velocity
because the mass is smaller.
D- The Law of Conservation
1- In a closed, isolated system, the total momentum must remain the same
2- During a collision or explosion, one object loses momentum and one object
gains momentum
3- Momentum gained must always equal the momentum lost
4- The total momentum before must always equal the total momentum after
a- 1  2 Problem (attached objects split into two)
b- 2  1 Problem (two objects come together)
c- 2 remains 2 Problem
5- Collisions
a- Elastic Collision- two objects collide and remain apart (2 remains 2),
momentum and kinetic energy are conserved
b- Inelastic collision- two objects collide and stick together (2 1),
momentum is conserved but kinetic energy is not
Topic 8: Work, Energy, and Simple Machines
I- Work
A- The product of the force exerted on an object and the distance the object moves in
the direction of the force
W = Work (J)
F = Force (N)
d = distance (m)
1- Work is a scalar quantity (magnitude only)
B- Work is only done if a force is exerted in the direction of motion and the object
moves (Work is done on an object only if the object moves in the direction of the
force)
C- If a force s exerted perpendicular to the motion, no work is done
1- If a force is exerted vertically upward to lift an object and the object is carried,
no work is done
2- What if a force is exerted at some other angle to the motion?
a- Pushing a lawnmower, pulling a wagon
b- Since the force (F) along the handle is not in the direction of motion, it is
not doing work on the wagon. When F is resolved into components, the
horizontal component (
is in the direction of motion and
therefore is doing the work on the wagon
(
c- Examples:
iLifting object- F is up, motion is up 
energy
,
 gains
ii-
Lowering object- F is up, notion is down
 loses energy
iii-
Carrying object horizontally- F is up, motion is to the side 
,
 no change in energy
II- Force vs. Displacement graph
A- Work can be calculated by dining the area under the force vs. displacement graph
III- Power
A- The rate at which work is done or energy is transferred
P = power (watts)
W = work (J)
t = time (s)
1- Since
,
=
B- Power is a scalar quantity
IV- Energy
A- The capacity for doing work
B- The ability to change an object or its environment
C- Changes can occur in several ways
1- Examples- speeding car, rubber band, bullet
D- Work Energy Theorem
1- The net (total) work done on an object is equal to its change in energy
2- If work is done on the object, the object gains energy (KE or PE)- object’s
energy increases
3- If work is done by the object, the object loses energy (KE or PE)- object’s
energy decreases
4- The energy that is gained or lost is always equal to the net work done on or by
the object
(
(include Q if friction is present)
a- If
is positive, energy is gained, if
is negative, energy is lost
V- Forms of Energy
A- Kinetic Energy (KE)- energy due to the motion of an object
B- Potential Energy (PE)- energy stored in an object because of its state (elongated
or compressed) or position (vertical)
VI- Kinetic Energy
VII-
KE = kinetic energy (J)
v = velocity (m/s)
m = mass (kg
A- Kinetic energy is a scalar quantity (magnitude only)
B- If an object is at rest, KE = 0 Joules
Gravitational Potential Energy
A- Energy stored in an object because of its position measured from a reference point
B- When work is done against gravity (lift), an object gains gravitational PE
C- When an object falls with gravity, the object loses gravitational PE
m = mass (kg)
g = acceleration due to gravity (
= height measured from a reference point (m)
D- Gravitational PE is measured from a reference point, PE at the reference point is 0
E- Scalar quantity- magnitude only
VIII- Elastic Potential Energy
A- The energy stored in a spring or rubber band when work is done in compressing
or stretching it
1- The compression or elongation of a spring is the change in spring length from
its equilibrium position
k = spring constant (N/m)
x = change in spring length from the equilibrium position (m)
B- Hooke’s Law
1- Provided the elastic limit of the spring is not reached, the compression or
elongation of the spring is directly proportional to the force applied
a- Increase force applied, increase elongation
IX- Graphs
A- Force vs. Elongation
-
Direct relationship
Slope = spring constant (k)
B- Elastic PE vs. Elongation
X- Conservation of Energy
A- Closed, Isolated System
1- Objects do not leave or enter
2- No external force acts on the objects
3- No work is done on the system
B- The Law of Conservation of Energy
1- Within a closed, isolated system, energy can change form, but the total
amount of energy remains the same
2- Energy can neither be created nor destroyed
3- The total energy of the system is the sum of the KE, PE and internal energy
(Q) at any point
4- The total energy always remains the same
aXI- Energy Conservation of a Pendulum
Work  Gravitational PE  KE  Gravitational
PE  KE  Gravitational PE
Height reached on both ends is the same (unless
work is done or energy is lost due to friction)
A- Maximum potential energy- at the ends
B- Maximum kinetic energy- middle
C- Halfway to the middle- KE = PE = total
D- Pendulum moving fastest in the middle- KE is greatest
E- Maximum PE = Maximum KE
Topic 9: Electricity
I- Electrostatics- the study of electrical charges that can be collected and held in one place
II- Current electricity- charges that continuously flow
III- Micro Structure and Matter
A- An atom is the smallest particle of an element that has all the element’s chemical
properties
B- Each atom can be broken into smaller pieces called subatomic particles
1- Proton
a- Location- inside the nucleus
b- Mass(equal to neutron)
c- Positive charge that is equal in magnitude but opposite in sign to the
charge carried by an electron
2- Neutron
a- Location- inside the nucleus
d- Mass(equal to proton)
b- Carries no charge
3- Electron
a- Location- outside the nucleus in clouds/energy levels
b- Mass(less than proton and neutron)
c- Negative charge
IV- Charged objects
A- All objects become charged through a transfer of electrons
1- A neutral object has an equal number of electrons and protons
2- A positively charged object has a deficency of electrons
3- A negatively charged object has an excess of electrons
B- Grounding- connecting a charged object to the earth to remove the object’s charge
1- Positive object- attracts electrons from the earth
2- Negative object- loses electrons to the earth
C- Electroscope- used to detect the presence of charge
1- When the leaves are neutral, they hang vertically
2- When the leaves are uncharged, they must be carrying charges of the same
sign and will diverge (go apart)
a- The leaves can never be oppositely charged
V- Transfer of charge
A- Electrons are the only particles that are free to transfer and they will only
transfer if there is a higher number of electrons on one object compared to
another
B- Law of Conservation of Charge- as electrons are transferred from one object
to another, the net charge must remain the same
C- Methods of Transfer
1- Friction- occurs when two objects are rubbed together, one object loses
electrons and one object gains electrons (fur +, rubber -)
2- Conduction- charging an object by transferring electrons during contact
with a charged object
a- Electrons move from one object to another
b- The charge received is always the same sign as that of the charging
object
3- Induction- a charged object causes a redistribution of the charges of
another object without contact
a- When the object is then connected to the ground, the object becomes
charged
i- The charge received is always the opposite charge of the charging
object
D- Objects gain or lose whole numbers of electrons
E- Elementary chargeF- The quantity of a charge that an object carries depends on the number of
unpaired electrons or protons in the material
G- Coulomb
1- Unit for charge
1C=
elementary charges
(Charge = number of protons/electrons x elementary charge
V- Coulomb’s Law
A- The magnitude of the force of repulsion or attraction is:
1- Directly proportional to the product of the charges
2- Inversely proportional to the square of the distance between them
electrostatic force (N)
electrostatic constant (
charge on object (C)
distance between center (m)
VI- Electric Fields
A- An electric field is the space surrounding a charged object through which a force
is exerted
B- Electric field is a vector quantity
1- Magnitude:
electrostatic force (N)
quantity of charge/charge in the field (C)
E = electric field intensity/strength (N/C)
2- Direction- the direction of an electric field is determined by looking at the
direction a small positive test charge would travel if placed in the field
a- A small test charge is used so as not to change the location of the charged
object
VII- Applications of Electric Fields
A- Introduction
1- When work is done on or by an object, the energy of the object changes
a- Change position- change PE
b- Change speed- change KE
2- Electrostatics is the study of charges at rest  changes in potential energy
3- Unlike charges attract
a- No work needs to be done on the charges to push them together
b- Work needs to be done on the charges to pull them apart
c- Work done on the charges increases their potential energy
4- Like charges repel
a- No work needs to be done on the charges to pull them apart
b- Work needs to be done on the charges to push them together
c- Worth done on the charges increases their potential energy
5- Potential energy of a charged object is called electric potential
6- Electrical potential difference- ant change in the potential energy of a charged
object
VIII- Electrical Potential Difference
A- Work done against an electric field per unit of charge
V = electrical potential difference (J/C = V)
W = work/electrical energy (J)
q = quantity of charge (C)
B- Electrical energy can be measured in electron volt (eV)
1- Electron volt- energy required to move 1 electron through a potential
difference of 1 volt
2C- Potential energy is always measured from a reference point
1- Reference point for electrical potential energy is a distance of infinity away
from the charged object
a- The test charge is located too far from the charged object to interact
IX- Electric Potential in a Uniform Field
A- The electric field intensity between oppositely charged parallel plates is uniform
throughout
1- Since E is uniform for oppositely charged parallel plates,
experienced by a
charge is the same anywhere in between the plates
B- Electric field intensity and potential difference measure qualities of an electric
field
1- Intensity- strength or magnitude
2- Potential difference- work per unit of charge needed to move the charge in the
field
C- Calculate the strength of the electric field between parallel plates:
E = electric field strength (V/m)
V = potential difference (V)
d = distance between the plates (m)
Topic 10: Current and Circuits
I- Introduction
A- When two conducting spheres are connected, electrons will flow from high
potential to low potential
B- Charges will stop flowing when the potentials become equal
C- How can we keep the electrons flowing?
1- To keep the charges flowing, a potential difference must exist between the
two spheres
a- Battery, solar cell, generator
II- Electric Current
A- Flow of electric charges (electrons)
B- The rate at which a quantity of charge flows past a point in a circuit
I = Current (ampere- A)
q = quantity of charge (C)
t = time (seconds)
C- Current is a scalar quantity
D- One ampere of current is the flow of one coulomb of charge each second
III- Conditions Necessary for Current
A- Circuit
1- Closed loop of conducting materials through which current flows
2- Must be closed at all points
B- Source of Potential Difference
1- Battery converts chemical energy to electrical energy
C- Photovoltaic cell (solar cell)- converts light energy to electrical energy
D- Generator- driven by moving water, rushing steam or the wind, converts kinetic
energy into electrical energy
IV- Resistance
A- A potential difference must exist between two points to keep electrons flowing
B- The circuit must consist of conducting materials and be closed at all points
C- The amount of current flowing depends on the potential difference and the
materials in the current
D- Resistance- the property that determines how much current will flow through
1- Determined by placing a potential difference (battery) across two points on a
conductor and measuring the current that flows
Slope of a voltage vs. current graph
is resistance
E- Ohm’s Law
1- The ratio of potential difference to current equals resistance
R = resistance (ohms)
V = potential difference (V)
I = current (A)
2- Resistance is a scalar quantity
3- Resistor- a device designed to have a specific amount of resistance
4- Variable Resistor- a device designed to change its resistance
5- Increase resistance, decrease current (indirect relationship)
F- Factors Affecting Resistance
1- Temperature
a- Temperature is a measure of the average kinetic energy of the molecules
b- Increase temperature, increase kinetic energy and the molecules move
faster
c- As the molecules move faster, it becomes more difficult for the electrons
to travel through (more resistance, less current)
d- Temperature and resistance are directly proportional
2- Length
a- The longer the resistor, the more molecules the electrons encounter as they
travel through
b- The increased number of molecules makes it more difficult for the
electrons to navigate through
c- Length and resistance are directly proportional
3- Cross-sectional area (thickness)
a- The thicker the resistor, the more empty space there is for the electrons to
travel
b- More empty space makes It easier for the electrons to navigate through
c- Thickness and resistance are indirectly proportional
4- Resistivity (material)
a- The ability of a material to create resistance
b- Resistivity and resistance are directly proportional
G- Calculations
R = resistance (ohms)
= resistivity (ohms m)
L = length (m)
A = cross- sectional area (m)
V- Electrical Power
A- Power measures the rate at which energy is transferred or work is done
B- One joule per second = one watt
C- The energy carried by a wire per second (p) depends on the charge per second (I)
and the energy of the charge (v)
P = VI V = IR
P=

P = Power (W)
V = Potential difference (V)
I = Current (A)
VI- Electrical Energy (Work)
A- Energy is the ability to do work
B- Electrical work- a measure of how much work can be done in the circuit
VII-
Series and Parallel Circuits
A- Series Circuits
1- Devices are connected in one single branch
2- Current only has one path to follow and therefore the current in each device
connected in series is the same
B- Parallel Circuit
1- Devices are connected in different branches
2- Current has more than one path to follow and therefore, the current in each
device connected in parallel is not the same unless the resistance of each
device is the same
C- Ammeter
1- Used to measure the current through any branch or part of a circuit
2- Resistance is very low so as not to affect the current in the circuit
3- Connected in the circuit (series)
D- Voltmeter
1- Used to measure the potential difference across some part of the circuit
2- Resistance is very high so as not to affect the current in the circuit
3- Connected outside the current in its own branch (parallel)
Topic 11: Magnetism
I- Magnetism
A- A force created by the movement of charge
B- Domain- area of material where all electrons are orbiting the same way to create a
magnetic field
1- Domains are pointing in random directions, zero net effect
2- Domains are pointing in the same direction- bar magnet
C- Iron, copper, and nickel can be easily magnetized
D- Types of magnets:
1- Permanent- domains are pointing in the same direction
2- Temporary- you can force the domains to match up but they do not naturally
3- A magnet always has two poles: North and South
II- Magnetic Fields
A- The area over which a magnet exerts a magnetic force
B- Can be created by: electron orbitals, current in a wire, induction (anytime charge
moves)
C- Magnetic Field Lines- drawn to represent a three dimensional magnetic field on
two dimensional paper
1- Represent the magnitude and direction of a magnetic field
2- Must never cross, have arrows, and form closed paths
3- Magnitude: Stronger magnetic field  more densely drawn lines
4- Direction: drawn from North to South
D- Magnetic north is the geographic south, magnetic south is the geographic north
1- North pole of a compass is attracted to the Earth’s magnetic south pole
(geographic north)
E- Magnetic Field Strength- the number of magnetic lines of flux per unit area
passing through a plane perpendicular to the direction of the lines
1- A vector quantity
Topic 12: Waves
I- Waves
A- Wave- a vibratory disturbance that propagates through a medium or field
1- Particles vibrate about an average position
B- Energy Transfer
1- Waves transfer energy from one place to another by repeated small vibrations
of particles of a medium or by repeated small changes in the strength of a field
2- No actual transfer of mass- only energy is transferred
3- Mechanical waves (sound and water) require a medium
4- Electromagnetic waves (visible light and radio waves) can travel through a
vacuum (a region of empty space)
C- Pulses and Periodic Waves
1- Pulse- a single short disturbance that moves from one position to another in a
field or medium
a- If it reaches a new medium, part of the pulse is transmitted, absorbed, and
reflected
iReflection- the rebounding of a pulse of wave as it strikes a barrier
iiIf the end of a rope was attached to a fixed unyielding body, the
pulse would be completely reflected- it would invert
2- Periodic Wave- series of regular repeated disturbances
D- Types of Wave Motion
1- Longitudinal wave- w wave in which the motion of the vibratory disturbance
is parallel to the direction of travel- sound waves
2- Transverse wave- motion of the vibratory disturbance is perpendicularelectromagnetic waves
II- Characteristics of Periodic Waves
A- Frequency- the number of cycles (compete vibrations) per unit of time
(waves/second)
1- Determines pitch of sound wave or color of light wave
B- Period- the time required for one complete vibration to pass a given point
(seconds/wave)- inverse of frequency
C- Amplitude- the maximum displacement of a particle of the medium from its rest
or equilibrium point- maximum change in field strength from its normal value
1- Crest- the maximum displacement of a particle of the medium in the positive
direction
2- Trough- the maximum displacement in the negative direction
a- Crests and troughs apply to transverse waves
3- Condensations- regions of maximum compression
4- Rarefactions- regions of maximum expansion
a- Condensations and rarefactions apply to longitudinal waves
5- Amplitude related to the amount of energy a wave transmits
a- The greater the amplitude of a light wave, the greater its intensity
(brightness)
D- Phase- points on successive wave curves of a periodic wave that are displaced
from their rest position by the same amount (in phase)
E- Wavelength- the distance between any two successive points in phase with one
another
F- Speed of Waves- equal to the product of the wave’s frequency and wavelength
v = velocity (m /s)
f = frequency (Hz)
= wavelength (m)
III- Periodic Wave Phenomena
A- Wave Fronts- all points on a wave that are in phase
B- Doppler Effect- the change in observed or apparent frequency and wavelength
due to the relative motion of a wave source and an observer
1- If the source is approaching the observer (vice versa), the frequency appears
to increase
2- If the source is receding from the observer (vice versa), the frequency appears
to decrease
3- Speed is not affected by the Doppler effect- the change in apparent
wavelength is inversely proportional to the change in apparent frequency
4- Can cause changes in the apparent pitch of a sound wave  higher frequency,
higher pitch
5- Human eye perceived light waves of different frequencies in different colors
a- Lowest frequency (longest wavelength) = red
b- Highest frequency (shortest wavelength) = blue violet
c- Apparent color of an approaching light source is shifted toward the blue
violet end of the spectrum, while that of a receding source is shifted
toward the red end
C- Interference
1- Superposition- two or more waves travel through the same medium
simultaneously
a- Principle of Superposition- the resultant displacement at any point is the
sum of the displacements of the individual waves
2- Interference- the superposition of one wave on another
a- Constructive Interference- occurs when the wave displacements of two inphase waves in the same medium are in the same direction
iResults in a greater amplitude
iiMaximum constructive interference occurs when waves are in
phase and crest superposes on crest (phase difference = 0 degrees)
iiiAntinodes- point of maximum displacement of a medium when
two waves are interacting
b- Destructive Interference- when two waves of equal frequency and
amplitude whose phase difference is 180 degrees (1/2 ) meet at a point
i-
Node- regions of zero displacement of a medium
D- Standing Waves- a pattern of wave crests and troughs that remains stationary in a
medium
1- Occurs when two waves having the same amplitude and frequency travel in
opposite directions through a uniform medium
E- Resonance- the vibration of a body at its natural frequency due to the action of a
vibrating source of the same frequency
1- Every elastic body has a natural frequency (particular frequency at which it
will vibrate if disturbed)
2- When a periodic force is applied to an elastic body, it absorbs energy and the
amplitude of its vibration increases  resonance
F- Diffraction- the spreading of waves into the region behind a barrier in the wave’s
path
IV- Light
A- Properties
1- Transverse, electromagnetic wave
2- Does not require a medium, but if it does travel through a medium the
particles vibrate perpendicular to the direction of the wave
3- Produced when an excited electron returns to a lower level
4- Travels in a straight line called a ray
5- Is approximately 10% of the electromagnetic spectrum
6- Ranges in wavelength from 400 to 700 nanometers
a- Shortest = violet, longest = red
B- Electromagnetic Spectrum- a list of all waves produced when an excited electron
returns to a lower level
1- Frequency determines the type of wave
a- High frequency- gamma (violet for visible light)
b- Low frequency- radio (red for visible light)
2- All electromagnetic waves travel at the same speed (c =
m/s)nothing can travel faster than c
C- Polarization- separation of a beam of light so that the vibrations are in the same
direction (only light waves can be polarized)
D- Ray Diagrams- show the direction of wave travel
1- Ray- a straight line that is drawn at right angles to a wave front any points in
the direction of wave travel
2- Incident ray- a ray that originates in a medium and strikes a boundary or an
interference with another medium
3- Reflected ray- a ray that has rebounded from a boundary or interference
4- Refracted ray- a ray that results from an incident ray entering a second
medium (bends)
E- Reflection of Light
1- Angle of Incidence ( - the angle between the incident ray and the normal to
the surface at the point where the ray strikes the surface
2- Angle of Reflection( - the angle the ray rebounds at- between the reflacted
ray and the normal to the surface at the point of reflection
3- Law of Reflection: the angle of incidence equals the angle of reflection
4- Total internal reflection- the angle of incidence is bigger than the critical angle
(you only have a critical angle if you are going from high to low index)
a- Critical angle- angle at which all light reflects
F- Refraction of Light
1- Refraction- the change in direction of a wave due to a change in speed at the
boundary between two different media
2- An angle at zero degrees may change speed upon entering a new medium, but
not direction
3- Light passes through a more dense medium- (low  high index – fast to slow)
refracts toward normal
4- Light passes through a less dense medium (high  low index- slow to fast)light refracts away from the normal
G- Absolute Index of Refraction- the ration of the speed of light in a vacuum to the
speed of light in a material medium
n = absolute index of refraction (no units)
c = speed of light in a vacuum (
v = speed (m/s)
1- The greater the index of refraction, the more dense the medium is and the
slower light travels in the medium
2- Frequency does NOT change as the wave enters a new medium
H- Snell’s Law- the mathematical relationship that governs the refraction of light as
it passes obliquely from one medium to another of different optical density
= angle of incidence (
where you are starting)
= angle of refraction (
where you are going)
I- Colors- different colors have different frequencies, different frequencies
experience different indices of refraction, therefore they experience different
amounts of bending
Topic 13: Modern Physics
I- Waves vs. Particles
A- Wave Model of Light
1- Light is an electromagnetic wave that transmits energy, with or without a
medium
2- Light has frequency, wavelength, amplitude, and velocity
a- Frequency/ wavelength determine type of wave or color
3- Amplitude- direct relationship with energy
4- Velocity- indirect relationship with index of refraction
5- Interference diffraction and polarization can only be explained if light travels
as a wave
II- Black Body Radiation
A- Max Plank theorized that electromagnetic radiation is emitted by the atoms of a
material
1- Atoms given energy in the form of heat, released as electromagnetic
radiation
2- Energy released directly proportional to frequency of electromagnetic
radiation
B- Quantum- discrete amount of energy
1- Quantum of light- photon
a- Massless, has energy and momentum
C- Planck’s Hypothesis
1- Energy of a photon is directly related to the frequency of the photon
energy of the photon (J)
h = Planck’s constant (
)
f = frequency of photon (Hz)
III- Photoelectric Effect
A- Photo = light, electric = current
B- A process whereby light (electromagnetic radiation) falling on a metallic, photoemissive surface forces the motion of electrons (current). Light strikes a photoemissive surface. Electrons in the surface absorb energy, causing them to leave
their atoms.
1- Excess energy becomes the kinetic energy of the emitted electron
a- Each electron is ejected by a single photon striking the surface
b- More photons = more current
C- How does the photoelectric effect show that light is a particle?
1- Electrons are only released when light is a certain frequency  individual
units of energy are coming into the surface. If light were a wave, only
amplitude would be related to it
D- Anomalous Behavior in Photoelectric Effect
1- Photoelectrons (electrons ejected from atoms due to photon energy) are not
released below a certain frequency, regardless of intensity of light
2- Threshold Frequency- minimum frequency of incident light necessary for a
material to emit electrons
3- The release of photoelectrons is instantaneous, even in very dim light,
provided that the frequency is above the threshold
IV- Models of the Atom
A- Reintroduction to Matter
1- Atom- smallest particle of an element that still retains the characteristics of
that element
2- Scientific conception of the atom has changed over the centuries as more
sophisticated means of study were developed
B- Thomson Plum Pudding Model
1- J.J. Thomson discovered that electrons have negative charge and very low
mass
2- Plum Pudding Model- uniform distribution of positive charge in which
individual electrons are embedded in a scattered way
C- Rutherford Model
1- Gold Foil Experiment
a- Shot alpha particles (helium nuclei) at a thin sheet of gold foil
b- Massive, positively charged particles (compared to single protons or
electrons)
c- While 99.9% of particles passed through the foil with no effect, 0.1% were
deflected due to Electrostatic Repulsion
d- Proved that nucleus existed, and had all of the atom’s positive charge
D- Bohr Model
1- Refinement of the Rutherford model
a- Explained atomic stability and bright line emission spectra
b- Electrons can only occupy specific orbitals of fixed radius
2- All forms of energy are quantized
a- Electrons can gain or lose energy, but only in fixed amounts (quanta)
b- Electrons gain or lose energy in the form of absorbed or emitted photons
3- Without gaining or losing energy, electrons remain in their orbits
4- Ionization potential- amount of energy needed for an electron to leave an atom
entirely
a- Missing one or more electrons, an atom becomes a positive ion
energy of emitted or absorbed photon
= initial energy of electron
= final energy of electrons
i- All are in Joules or eV (as long as they are consistent)
E- Cloud Model
1- Replacement/Refinement of the Bohr Model
a- Electrons are not confined to specific orbitals, but instead to clouds of
probability
b- Functionally similar to Bohr model, but more conceptually accurate
2- Accounts for the wave nature of subatomic particles
V- The Nucleus and Subatomic Particles
A- The Nucleus
1- Discovered by Rutherford via gold foil experiment
a- Has most of the atom’s mass
b- Nucleons- protons and neutrons
2- Average distance protons in nucleus:
m
a-
230 N (repulsive),
(attractive)
3- The Strong Force
a- Attractive force that binds the nucleus together
b- 100 times stronger than electrostatic force
c- Diminishes rapidly with distances larger than
m
d- Strongest of the four forces known to exist (strong, electromagnetic, weak,
gravity)
4- The Weak Force
a- Responsible for radioactive decay and solar fusion
b- Even shorter range,
m
c- Second weakest of the four fundamental forces (after gravity)
B- Einstein
1- Showed that matter and energy are just two different expressions of the same
basic things
E = energy (J)
m = mass (kg)
c = speed of light in a vacuum (
2- Shortcut- universal mass unit:
m/s)
, or 1/12 of one carbon atom
1 u of mass converts to 931 MeV of energy
C- The Nucleus and Energy
1- Since matter can become energy and vice versa, neither is necessarily
conserved
a- When nucleons come together to form atoms, some mass turns into energy
b- To break up a nucleus, significant work (energy) must be invested, which
becomes mass
VI- Classification of Matter
A- Particles are classified based on the types of interactions they have with other
particles
B- Leptons
1- No internal structure
2- Mass less than a proton
3- Each has a corresponding anti particle
a- Identical except for charge and magnetic properties (opposite charge)
C- Hadrons
1- Have internal structure (quarks)
2- Subdivided into:
a- Baryons- made of three quarks each, mass equal to or greater than a proton
b- Mesons- made of two quarks each (quark and anti-quark), highly unstable
D- Quarks
1- Possess fractional elemental charges
2- Building blocks of all hadrons
3- Six varieties- up (u), down (d), charm (c), strange (s), top (t), bottom (b)
a- Each has a corresponding anti-quark with opposite charge
E- Anti-Particles
1- Every particle has an anti-particle
a- Same mass, opposite charge
b- Denoted by a bar over the symbol
c- Matter composed of anti-particles  anti-matter
2- Positron- anti-electron