A rope of uniform linear density p and mass m is wrapped one complete turn around a hollow cylinder of mass M and radius R. The cylinder rotates freely about its axis as the rope unwraps (Figure 9-9). The rope ends are at x = 0 (one fixed, one loose) when point Pis at 0 0, and the system is slightly dis- placed from equilibrium at rest. Find the angular velocity as a function of angular displacement of the cylinder. -

A rope of uniform linear density p and mass m is wrapped one complete turn around a hollow cylinder of mass M and radius R. The cylinder rotates freely about its axis as the rope unwraps (Figure 9-9). The rope ends are at x = 0 (one fixed, one loose) when point Pis at 0 0, and the system is slightly dis- placed from equilibrium at rest. Find the angular velocity as a function of angular displacement of the cylinder. -