Final answer:
When a child gets off a rotating merry-go-round, the angular velocity of the merry-go-round remains the same. The child's jump does not change the total angular momentum of the system.
Step-by-step explanation:
When a child gets off a rotating merry-go-round, the angular velocity of the merry-go-round will remain the same, regardless of the direction the child jumps. This is because the child is not exerting any external torque on the merry-go-round.
Angular momentum is a property of rotating objects and is conserved unless an external torque is applied. In this case, the child's jump does not change the total angular momentum of the system (merry-go-round + child).
Therefore, the answer to all parts (a), (b), (c), and (d) is that the angular velocity of the merry-go-round remains the same.