AP Physics C

Mechanics Review

Kinematics – 18%Chapters 2,3,4

• 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

Constant Acceleration

2

2

dt

rd

dt

dva

dt

drv

xavv

dtvatd

atvv

2

2

1

20

2

002

0

r

vac

2

Centripetal Acceleration

Motion Equations

Newton’s Laws of Motion – 20%Chapters 5 & 6

• Newton’s Three Laws of Motion– Inertia– Fnet = ma – Equal and opposite forces

• 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 MotionSecond Law Problems

• Newton’s Second Law – – 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

maFnet

Newton’s Laws of MotionCircular 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

rmr

vmmaF c

22

Newton’s Laws of MotionAir Resistance – Drag Force

• Identify forces and draw free body diagrams• May involve a differential equation

– Example:

• 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

kvdt

dvmma

kvFD

Work, Energy, Power – 14%Chapters 7 & 8

• 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 PowerKey Equations

KW

mvK

t

W

dt

dWP

dFW

dxFW

2

2

1

Work

Work by a Constant Force

Power

Kinetic Energy

Work-Energy Theorem

Work, Energy and PowerKey Equations

2

2

1kxU

mghUdx

dUFFdxU

WU

s

g

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

dx

dUF

Systems & Linear Momentum – 12%Chapters 9 & 10

• Center of Mass• Linear Momentum• Conservation of Momentum• Internal vs. External forces• Collisions – Inelastic, Elastic• Impulse

Systems & Linear MomentumKey Equations

FdtpJ

pp

mvpm

mr

mm

xmxmx

fi

cm

cm

r

...

...

21

2211

Center of Mass

Momentum

Conservation of Momentum

Impulse

Systems & Linear MomentumCenter 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 MomentumCollisions

• 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 MomentumImpulse

•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 MomentumConservation of Momentum

• Momentum will always be conserved unless an outside force acts on an object.

• Newton’s Second Law could read:

• 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

dt

dpF

Circular Motion and Rotation – 18%Chapters 11 & 12

• 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 RotationBasic Rotational Equations

2

2

dt

d

dt

d

dt

d

2

2

1

22

0

2

o

oo

t

tt

Angular Velocity & AccelerationCircular Love and Angular Kinematics

Circular Motion and RotationLinear to Rotation

ra

rv

rx

As a general rule of thumb, to convert between a linear and rotational quantity, multiply by the radius r

vmrprl

Fr

Circular Motion and RotationRolling and Kinetic Energy

• A rolling object has both translational and rotational kinetic energy.

22

2

2

1

2

12

1

mvIK

IK

roll

rot

Circular Motion and RotationMoment of Inertia

rdmmrI 2

2mhII cm cmI

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

2mh

I for the Center of Mass

m – total mass

H – distance from com to axis of rotation

Circular Motion and RotationMoment 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

rodmm IIII 21

m1 m2

L

Axis of rotation

222

12

1

22

21 LM

Lm

LmI rod

Circular Motion and RotationTorque

• 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

sinrFFr

Circular Motion and RotationAngular Momentum

Il

vmrprl

•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 RotationNewton’s 2nd Law for Rotation

net

net

dt

dL

I

Oscillations and Gravity – 18%Chapters 14 & 16

• 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

• Knowing the acceleration you can find ω.

xxa 2)(

OscillationsSprings and Simple Pendulums

k

mTs 2

Ideal Spring

g

lTp 2

Simple Pendulum

OscillationsPhysical 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.

mgh

ITp 2

Oscillations and Gravity – 18%Chapters 14 & 16

• Law of Gravitation• Superposition – find force by adding the force from each individual object

• 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

GravityA very serious matter

r

Gmv

r

mGmU

r

mGmF

g

g

21

221 Universal Law of Gravity

Gravitational Potential Energy

Circular Orbit Speed