AP Physics C Rotational Motion Equations

Torque Equation

F x Lever arm

Another Torque Equation

I α

Center of mass

1/M ∑rm

or

1/M ∫r dm

Parallel axis theorem

I=Icm+md²

Inet

I=I₁ + I₂ +I₃

kinematic equation changes

x = θ

w = ω

a = α

counterclockwise.....clockwise

+...-

x to θ

x=rθ

v to ω

v=rω

a(tan) to α

a=rα

a(c) or a(radial)

rω²

Point mass m at a distance r from the axis of rotation.

I=mr²

Rod of length L and mass m

(Axis of rotation at the end of the rod)

I= ¹/₃ mL²

Rod of length L and mass m (through the center)

I= ¹/₁₂ mL²

Thin circular hoop (or cylindrical shell) of radius r and mass m

I = mr²

Thin, solid disk (or solid cylinder) of radius r and mass m

I= ¹/₂ mr²

Donut

I= ¹/₂ m(r₁²+r₂²)

1-D object

L (length)

2-D or 3-D object

r (radius)

L

Iω