A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. A merry-go-round is initially at rest, has a radius R = 1.2 meters, and a mass M = 261 kg. A small boy of mass m = 47 kg runs tangentially to the merry-go-round at a speed of v = 1.6 m/s and jumps on.

a. Calculate the moment of inertia of the merry-go-round in kg m^{2}.

b. Immediately before the boy jumps on the merry-go-round, calculate his angular speed (in radians second) about the central axis of the merry-go-round.

c. Immediately after the boy jumps on the merry-go-round, calculate the angular speed in radians/second of the merry-go-round and boy.

d. The boy then crawls towards the center of the merry-go-round along a radius. What is the angular speed in radians/second of the merry-go-round when the boy is half way between the edge and the center of the merry-go-round?

e. The boy then crawls towards the center of the merry-go-round. What is the angular speed in radians/second of the merry-go-round when the boy is at the center of the merry-go-round?

f. Finally, the boy decides that he has had enough fun. He decides to crawl to the outer edge of the merry-go-round and jump off. Somehow, he manages to jump in such a way that he hits the ground with zero velocity with respect to the ground. What is the angular speed in radians/second of the merry-go-round after the boy jumps off?