Question

A uniform solid cylinder of mass m and radius R is set in rotation about its axis with an angular velocity ω_o, 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.

Answer 1

(a) Let us depict the forces acting on the cylinder and their point of applications for the cylinder and indicate positive direction of x and φ as shown in the figure. From the equations for the plane motion of a solid