Problem 1.262

A uniform solid cylinder of mass \(m\) and radius \(R\) is set in rotation about its axis with an angular velocity \(\omega_{0}\), then lowered with its lateral surface onto a horizontal plane and released. The coefficient of friction between the cylinder and the plane is equal to \(k\). Find: (a) how long the cylinder will move with sliding; (b) the total work performed by the sliding friction force acting on the cylinder.