A uniform circular cylinder of mass M and radius a can rotate freely about its axis of symmetry which is fixed in a vertical position. A light string is wound around the cylinder so that it does not slip and a particle of mass m is attached to the free end. Initially the system is at rest with the free string taut, horizontal and of length b. The particle is then projected horizontally with speed u at right angles to the string. The string winds itself around the cylinder and eventually the particle strikes the cylinder and sticks to it. Find the final angular speed of the cylinder.