AP Physics C Rotation

random formulas

Torque in terms of angular momentum

dL/dt

Angular impulse

Integral of torque over time or change in angular momentum

K_rot

(1/2)Iw²

v

wr

Precession (omega)

(Mgr)/(Iw) = torque/L

torque

r x F

components of a

a_t = alpha * r, a_r = v²/r

I

integral r² dm, dm=lambda dx, alpha dA, p dV, etc.

parallel-axis theorem

I=I_cm + Mh²

W

integral torque dtheta

P

dW/dt = torque * w

L

r x p

I for Thin-walled Hollow Cylinder about central diameter

MR²

I for Solid Cylinder about central diameter

(1/2)MR²

I for Rectangular Plate, axis perpendicular to and through center

(1/12)M(a²+b²)

I for Slender Rod, axis through center of midpoint

(1/12)ML²

I for Slender Rod, axis through one end parallel to midpoint

(1/3)ML²

I for Solid Sphere about diameter

(2/5)MR²

I for Thin-walled Hollow Sphere about diameter

(2/3)MR²

I for Thin Rectangular Plate, axis along edge (a is length [perp. to axis of rotation] of plate)

(1/3)Ma²