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 = 1.3 meters, and a mass M = 291 kg. A small boy of mass m = 42 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on. Randomized Variables R = 1.3 meters M = 291 kg m = 42 kg v = 1.8 m/s 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.
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 = 1.3 meters, and a mass M = 291 kg. A small boy of mass m = 42 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on.
Randomized Variables
R = 1.3 meters
M = 291 kg
m = 42 kg
v = 1.8 m/s
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 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?
Part 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?
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 is the angular speed in radians/second of the merry-go-round after the boy jumps off?
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