A merry-go-round is a playground ride that consists of a large disk mounted to t

Question

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 = 201 kg. A small boy of mass m = 46 kg runs tangentially to the merry-go-round at a speed of v = 1.8 m/s, and jumps on.
(a-d in earlier post.)

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?

Explanation / Answer

e)

angular speed of boy

W1=1.8/1.3=1.3846 rad/sec

By Conservation of angular momentum

I1W1=I2W2

(mR2)W1 =(MR2/2)W2

(46*1.32)*1.3846 =(201*1.32/2)*W2

W2=0.634 rad/sec

f)

By Comservation of angular momentum

I1W1=I2W2

(mR2)W1=(mR2+MR2/2)W2

(46*1.32)*1.3846 =(46*1.32+201*1.32/2)*W2

W2=0.4348 rad/sec

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