Problem 3: An ice skater is spinning at 5.2 rev/s and has a moment of inertia of 0.24 kg m2. Part (a) Calculate the angular momentum, in kilogram meters squared per second, of the ice skater spinning at 5.2 rev/s. Part (b) He reduces his rate of rotation by extending his arms and increasing his moment of inertia. Find the value of his moment of inertia (in kilogram meters squared) if his rate of rotation decreases to 0.75 rev/s. Part (c) Suppose instead he keeps his arms in and allows friction of the ice to slow him to 2.5 rev/s. What will be the magnitude of the average torque that was exerted, in N m, if this takes 18 s?

problem5: 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. The merry-go-round shown is initially at rest, has a radius R = 1.2 meters, and a mass M = 296 kg. A small boy of mass m = 46 kg runs tangentially to the merry-go-round at a speed of v = 1.3 m/s, and jumps on. Part (a) Calculate the moment of inertia of the merry-go-round, in kg m2. Part (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. Part (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. Part (d) The boy then crawls towards the center of the merry-go-round along a radius. What will be 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? Part (e) The boy then crawls to the center of the merry-go-round. What will be the angular speed in radians/second of the merry-go-round when the boy is at the center of the merry go round? Part (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 will be the angular speed in radians/second of the merry-go-round after the boy jumps off?