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AP Physics C
Mechanics Review
Kinematics – 18%
Chapters 2,3,4
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Position vs. displacement
Speed vs. Velocity
Acceleration
Kinematic Equations for constant acceleration
Vectors and Vector Addition
Projectile Motion – x,y motion are independent
Uniform Circular Motion
Kinematics –
Motion in One and Two Dimensions
• Key Ideas and Vocabulary
– Motion in the x is independent from motion in the y
– Displacement, velocity, acceleration
– Graphical Analysis of Motion –
• x vs. t - Slope is velocity
• v vs. t - Slope is acceleration
- Area is displacement
• a vs. t – Can be used to find the change in velocity
– Centripetal Acceleration is always towards the center
of the circle
Kinematics –
Motion in One and Two Dimensions
Motion Equations
dr
v
dt
dv d 2 r
a
 2
dt dt
Constant Acceleration
v  v0  at
1 2
d  at  v0t  d 0
2
2
2
v  v0  2ax
2
Centripetal Acceleration 
v
ac 
r
Newton’s Laws of Motion – 20%
Chapters 5 & 6
• Newton’s Three Laws of Motion
– Inertia
– Fnet = ma
– Equal and opposite forces
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Force
Weight vs. Mass
Free Body Diagrams
Tension, Weight, Normal Force
Friction – Static and Kinetic, Air Resistance
Centripetal Forces and Circular Motion
Drag forces and terminal speed
Newton’s Laws of Motion
Second Law Problems
• Newton’s Second Law – Fnet  ma
– Draw free body diagram identifying forces on a
single object
– Break forces into components
– Apply 2nd Law and solve x & y components
simultaneously
– Inclined Plane –
• Rotate axes so that acceleration is in the same direction
as the x-axis
Newton’s Laws of Motion
Circular Motion Problems
• Draw free body diagram identifying forces on a single
object
• Break forces into components
• Apply 2nd Law and solve x & y components
simultaneously
• Remember that the acceleration is centripetal
and that it is caused by some force
v2
F  mac  m  m 2 r
r
Newton’s Laws of Motion
Air Resistance – Drag Force
• Identify forces and draw free body diagrams
• May involve a differential equation
– Example:
FD  kv
dv
ma  m  kv
dt
• Separate variables and solve. Should end up with
something that decreases exponentially
• Terminal Velocity – Drag force and gravity are equal
in magnitude – Acceleration is equal to zero
Work, Energy, Power – 14%
Chapters 7 & 8
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Kinetic Energy
Work – by constant force and variable force
Spring Force
Power
Potential Energy – gravitational, elastic
Mechanical Energy
Conservation of Energy
Work Energy Theorem
Work, Energy and Power
Key Equations
W   F  dx
Work
W  F d
Work by a Constant Force
dW W
P

dt
t
1 2
K  mv
2
W  K
Power
Kinetic Energy
Work-Energy Theorem
Work, Energy and Power
Key Equations
U  W
dU
U    Fdx  F  
dx
U g  mgh
1 2
U s  kx
2
Potential Energy Curves
•Slope of U curve is –F
•Total energy will be given,
the difference between total
energy and potential energy
will be kinetic energy
dU
F 
dx
Systems & Linear Momentum – 12%
Chapters 9 & 10
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Center of Mass
Linear Momentum
Conservation of Momentum
Internal vs. External forces
Collisions – Inelastic, Elastic
Impulse
Systems & Linear Momentum
Key Equations
m1 x1  m2 x2  ...
xcm 
m1  m2  ...
mr
rcm 
m
p  mv
Center of Mass
Momentum
pi  p f
Conservation of Momentum
J  p   Fdt
Impulse
Systems & Linear Momentum
Center of Mass, Internal and External forces
• Center of Mass can be calculated by summing
the individual pieces of a system or by
integrating over the solid shape.
• If a force is internal to a system the total
momentum of the system does not change
• Only external forces will cause acceleration or
a change in momentum.
• Usually we can expand the system so that all
forces are internal.
Systems & Linear Momentum
Collisions
• Inelastic collisions – (objects stick together)
– Kinetic energy is lost
– Momentum is conserved
• Elastic Collisions – (objects bounce off)
– Kinetic energy is conserved
– Momentum is conserved
Systems & Linear Momentum
Impulse
•Impulse is the change in momentum
•Momentum will change when a force is applied to
an object for a certain amount of time
•Area of Force vs Time curve will be the change in
momentum
Systems & Linear Momentum
Conservation of Momentum
• Momentum will always be conserved unless an outside force
acts on an object.
• Newton’s Second Law could read:
dp
F
dt
• Newton’s Third Law is really a statement of conservation of
momentum
• Set initial momentum equal to final momentum and solve –
make sure to solve the x and y components independently
Circular Motion and Rotation – 18%
Chapters 11 & 12
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Uniform Circular Motion (chap 4 & 6)
Angular position, Ang. velocity, Ang. Acceleration
Kinematics for constant ang. Acceleration
Relationship between linear and angular variables
Rotational Kinetic Energy
Rotational Inertia – Parallel Axis Theorem
Torque
Newton’s Second Law in Angular form
Circular Motion and Rotation – 18%
Chapters 11 & 12
• Rolling bodies
• Angular momentum
• Conservation of Angular momentum
Circular Motion and Rotation
Basic Rotational Equations
Angular Velocity & Acceleration
d

dt
d d 2 

 2
dt
dt
Circular Love and Angular
Kinematics
1 2
  t   o t   o
2
   0  t
  o  2
2
2
Circular Motion and Rotation
Linear to Rotation
As a general rule of thumb, to convert between a
linear and rotational quantity, multiply by the radius r
x  r
v  r
a  r
  rF
l  r  p  mr  v
Circular Motion and Rotation
Rolling and Kinetic Energy
• A rolling object has
both translational and
rotational kinetic
energy.
1 2
K rot  I
2
1 2 1 2
K roll  I  mv
2
2
Circular Motion and Rotation
Moment of Inertia
I   mr   rdm
2
How something rotates will depend on the mass
and the distribution of mass
Parallel Axis Theorem – allows us to calculate I for an
object away from its center of mass
I  I cm  mh
2
I cm
mh
2
I for the Center of Mass
m – total mass
H – distance from com to
axis of rotation
Circular Motion and Rotation
Moment of Inertia
• For objects made of multiple pieces, find the moment
of inertia for each piece individually and then sum
the moments to find the total moment of inertia
Axis of rotation
m1
m2
L
I  I m1  I m 2  I rod
2
2
1
L
L
I  m1   m2   M rod L2
2
 2  12
Circular Motion and Rotation
Torque
  r  F  rF sin 
• Rotational analog for force – depends on the force
applied and the distance from the axis of rotation
• If more than one torque is acting on an object then
you simply sum the torques to find the net torqu
Circular Motion and Rotation
Angular Momentum
l  r  p  mr  v
l  I
•Angular momentum will always be conserved in the
same way that linear momentum is conserved
•As you spin, if you decrease the radius (or I) then you
should increase speed to keep angular momentum
constant
Circular Motion and Rotation
Newton’s 2nd Law for Rotation
 net  I
dL
  net
dt
Oscillations and Gravity – 18%
Chapters 14 & 16
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Frequency, Period, Angular Frequency
Simple Harmonic Motion
Period of a Spring
Pendulums
– Period
– Simple
– Physical
Oscillations
• All harmonic motion will can modeled by a sine
function
• The hallmark of simple harmonic motion is
a( x)   x
2
• Knowing the acceleration you can find ω.
Oscillations
Springs and Simple Pendulums
Ideal Spring
Simple Pendulum
m
Ts  2
k
l
T p  2
g
Oscillations
Physical Pendulum
A physical pendulum is
any pendulum that is
not a string with a mass
at the end. It could be a
meter stick or a possum
swinging by its tail.
I
Tp  2
mgh
Oscillations and Gravity – 18%
Chapters 14 & 16
• Law of Gravitation
• Superposition – find force by adding the force from each individual object
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Shell Theorem – mass outside of shell doesn’t matter
Gravitational Potential Energy
Orbital Energy – Kinetic plus Potential
Escape Speed
Kepler’s Laws’
– Elliptical Orbits
– Equal area in equal time (Cons. of Ang. Momentum)
– T2 α R3 - can be found from orbital period and speed
Gravity
A very serious matter
Gm1m2
Fg 
2
r
Gm1m2
Ug  
r
Gm
v
r
Universal Law of Gravity
Gravitational Potential Energy
Circular Orbit Speed