Figure shows a pulley in the shape of a uniform disk with a heavy rope hanging over

Question:

Figure shows a pulley in the shape of a uniform disk with a heavy rope hanging over it. The circumference of the pulley is 1.2 m and its mass is 2.2 kg. The rope is 8.0 m long and its mass is 4.8 kg. At the instant shown in the figure, the system is at rest and the difference in height of the two ends of the rope is 0.6 m.

(a) What is the angular velocity of the pulley when the difference in height between the two ends of the rope is 7.2 m?

(b) Obtain an expression for the angular momentum of the system as a function of time while neither end of the rope is above the center of the pulley. There is no slippage between rope and pulley.

0.6 m