Problem 1.243

A light thread with a body of mass \(m\) tied to its end is wound on a uniform solid cylinder of mass \(M\) and radius \(R\) (Fig. 1.55). At a moment \(t=0\) the system is set in motion. Assuming the friction in the axle of the cylinder to be negligible, find the time dependence of (a) the angular velocity of the cylinder; (b) the kinetic energy of the whole system.