Problem 15. A rope is wrapped around a fixed pulley of moment of inertia I and radius R.The rope then connects to a mass M. The mass is released from

rest and the rope begins to smoothly unwind from the pulley. (a) Draw a free body diagram for the pulley and one for the mass. Determine an expression (in terms of whatever variables are needed) for the time it takes the pulley to rotate through an angle 0. (b) Simply your answer to (a) if I = 3MR². You may use this for the remaining parts as well. (c) Determine the angular velocity of the pulley at the instant it has rotated through that angle 0. (d) Verify your answer to (c) by using energy conservation to do the same calculation.

Fig: 1