Question-

A pulley of moment of inertia I and radius r is fixed to a wall. A rope is wrapped around it and tied to a block of mass m. The block is initially held at rest, and then it is released. The block drops a distance h. The rope does not slip on the pulley, and the magnitude of the acceleration due to gravity is g. You know I, r, m, h, and g.

1. What is the work done by gravity on the system?

2. What is the change in potential energy of the system?

3. What is the change in kinetic energy of the system?

4. Write the equation that expresses the no-slip condition-the relationship between the linear and angular speeds.

5. What is the speed v of the block in terms of I, r, m, h, and g?

6. What is the angular speed w of the pulley in terms of I, r, m, h and g?