A "merry-go-round" consists of a large flat disc that is free to rotate around its center; children can spin it, climb on it, and so on. Suppose that a particular merry-go-round has a radius of 2m and a rotating mass of 100 kg. A child with a mass of 40 kg runs and jumps on its rim; he lands on it while moving tangentially at 3 m/s.
(a) What is the angular velocity of the platform after the child jumps on it?
(b) Suppose the child then walks to the center. What is the angular velocity then?