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 = 1.5 meters, and a mass M = 251 kg. A small boy of mass m = 41 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on. Randomized VariablesR = 1.5 meters M = 251 kg m = 41 kg v = 1.8 m/s (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. (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.
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 = 1.5 meters, and a mass M = 251 kg. A small boy of mass m = 41 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on.
Randomized VariablesR = 1.5 meters
M = 251 kg
m = 41 kg
v = 1.8 m/s
(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.
(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 to 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?
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