A rough cylinder, of mass M, is capable of motion about its axes, which is horizontal; a particle of mass m is placed on it vertically above the axis and the system is slightly disturbed. Show that the particle will slip on the cylinder when it has moved through an angle given by μ (M + 6m) cos 0 - M sin 0 = 4mu, where u is the coefficient of friction.

A rough cylinder, of mass M, is capable of motion about its axes, which is horizontal; a particle of mass m is placed on it vertically above the axis and the system is slightly disturbed. Show that the particle will slip on the cylinder when it has moved through an angle given by μ (M + 6m) cos 0 - M sin 0 = 4mu, where u is the coefficient of friction.