A 30-kg child runs around the edge of a playground merry-go-round. The merry-go-

Question

A 30-kg child runs around the edge of a playground merry-go-round. The merry-go-round has a mass of 200 kg and a radius of 2.0 m. Consider it to be a uniform solid disk for which I = 1/2 mr^2. The child is observed to be running, relative to the Earth, at a speed of 3.0 m/s while the merry-go-round rotates in the opposite direction making one revolution every -sec. (a) If the child stops running, what is the angular speed of the child plus merry-go-round combination? (b) How much work is done as the child stops running?

Explanation / Answer

M = 30 kg , r = 2 m , I = 0.5 mr^2

v = 3 m/s

T = 12 s

w = 2*3.14/12 = 0.523 rad/s

(a) from conservation of angularmomentum

Im*w+Mvr = (Im+Ic)wf

(0.5*mr^2*w) +Mvr = (0.5*mr^2 + mr^2)wf

(0.5*200*2^2*0.523)- (30*3*2) = (0.5*200*2^2 +30*2^2)wf

wf = 0.056 rad/s

(b) W = Ki - Kf = 0.5Im*w^2 +0.5mv^2 - 0.5(Im+Im)wf^2

W = (0.5*0.5*200*2^2*0.523^2) +(0.5*30*3^2) - (0.5* (0.5*200*2^2 +30*2^2)*0.056^2)

W = 189 J

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