Question

4. A solid cylinder of mass M and radius R has a rope wrapped around it and is hung off a ledge. The rope runs over a pulley which is a solid disc of mass m=M/4 and radius r=R/3 and then wraps around another solid cylinder of mass M/3 and radius R/2. When the system is released, the hanging cylinder begins to fall as the rope unwinds without slipping, and the smaller cylinder begins to roll without slipping to the right (again, with the rope unwinding without slipping).

1. Draw free body diagrams for the cylinders and pulley, and indicate the coordinate systems used for force and torque.

2. Solve for the acceleration of the rolling cylinder.

Answer 1