A 39.5 kg child stands at the center of a 125 kg playground merry-go-round which rotates at 3.10 rad/s. If the child moves to the edge of the merry-go-round, what is the new angular velocity of the system? Model the merry-go-round as a solid disk

Question

Physics

Diana Merritt

30 January, 00:57

A 39.5 kg child stands at the center of a 125 kg playground merry-go-round which rotates at 3.10 rad/s. If the child moves to the edge of the merry-go-round, what is the new angular velocity of the system? Model the merry-go-round as a solid disk

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Antony Blanchard · Answer 1

Using the law of conservation of angular momentum, we have

I1 w1 = I2 w2

ie., m1r^2/2 x w1 = (m1r^2/2 + m2r^2) w2

ie., new angular velocity w2 = m1 w1 / (m1 + 2m2) = 125 x 3.1 / (125 + 2 x39.5)

= 1.8995 = 1.9 rad / sec (nearly)