A “merry-go-round” consists of a large flat disc that is free to rotate around i

Question

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 2 m 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?
Please show all work.

Explanation / Answer

as there is no external torque on the child + merry-go-round system

so angular momentum of this system will be conserved

=> Linitial = Lfinal

a) mvR = (mR^2+MR^2/2)*W

=> 40*3*2 = (40*2^2 + (100*2^2)/2)*W

=> W = 0.666 rad/s

b)  mvR = (0+MR^2/2)*W

40*3*2 = (100*2^2)/2)*W

=> W = 1.2 rad/s

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