AP Physics
Chapter 10 Summary
Section 10.2: Rotational Variables
θ (theta) – angular displacement – radians
ω (omega) – angular velocity – radians/sec
α (alpha) = angular acceleration – radians/sec 2 t – still time and still in seconds
Measuring Angular Displacement - θ = L/r
360° = 2π radians = 1 revolution v= ωr :Linear velocity = angular velocity x radius a = αr: Linear acceleration = angular acceleration x radius
Sections 10.3 – 10.5
Linear
V = v
0
+at x = v
0 t+½at 2
V 2 = v
0
2 +2ax
Angular
ω=ω
0
+άt
θ=ω
0 t+½άt 2
ω 2 =ω
0
2 +2άθ
ω avg
=(ω
0
+ω f
)/2 V avg
= (v
0
+v f
)/2
Section 10.6: Kinetic Energy of Rotation
The rotational inertia of an object depends upon its shape and its mass. Values of I are always some form of the equation I=_mr 2 where the blank represents some fraction.
Torque = Iα = rotational inertia x angular acceleration. Hence Fr = Iα.
The Kinetic Energy of a rotating body is given by K = ½Iω 2 .
Section 10.7: Calculating Rotational Inertia
I = ∫ r2 dm
For various objects the results of these calculations can be found on page 253 in table 10.2
Parallel axis Theorem
If you know the I value for a body through the center of mass then a shortcut to finding its I value for a parallel axis is given as:
I = I cm
+ Mh
2
Where h is the perpendicular distance between the axes.
Section 10.8: Torque
Torque = Fr = force x radius. Torque is measured in newton•meters which means that it has the same units as work in a linear system.

Section 10.9: Newton’s Second Law for Rotation
Like force in a linear system, torque can be summed in order to solve problems.
∑τ = clockwise τ - counterclockwise τ = Fr = Iα
Section 10.10: Work and Rotational Kinetic Energy
Displacement
Velocity
Linear x v = dx/dt
Rotation about a fixed axis
Angular Displacement Θ
Acceleration
Mass (translational inertia) m
Force
Work
Kinetic Energy
Power
Linear Momentum a =dv/dt
F = ma
W = ∫F dx
K = ½ mv 2
P = W/t = Fv
ρ=mv
Angular Velocity
Angular Acceleration
Rotational Inertia
Torque
Work
Kinetic Energy
Power
Angular Momentum
ω=dθ/dt
α=dθ/dt
I
τ=Iα
W = ∫τ dθ
K= ½ Iω 2
P = τω
L = Iω