A rectangle of height 2a and width 2b rests on top of a fixed cylinder of radius R (see Fig.). The moment of inertia of the rectangle around its center is I. The rectangle is given an infinitesimal kick, and then ??rolls?? on the cylinder without slipping. Find the equation of motion for the tilt angle of the rectangle. Under what conditions will the rectangle fall off the cylinder, and under what conditions will it oscillate back and forth? Find the frequency of these smalloscillations.

b R 2a