A rigid body of mass and radius has rotational inertia

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A rigid body of mass

m

and radius

r

has rotational inertia

I = k m r^{2}

, where

k

is a dimensionless constant that depends on the object’s shape. The body is released from rest on a plane inclined at an angle

\theta

to the horizontal and rolls without slipping. Derive an expression for the magnitude of its translational acceleration in terms of

g

\theta

, and

k