A childrens playground merry-go-round can be regarded as a uniform horizontal di

Question

A childrens playground merry-go-round can be regarded as a uniform horizontal disk of radius 2.0 m and of mass 200 kg. A child of mass 30 kg is standing on the edge of the disk and the merry-go-round is rotating with a period of 6 seconds. The child now walks quickly into the centre so that their new position can be regarded as on the vertical axis of rotation. The rotation period changes. (a) Explain what physics principle governs the change in rotation speed? (b) Calculate the value of the new rotation period.

Explanation / Answer

Part A)

This is conservation of angular momentum

Part B)

Iw = Iw

Initial I = Disk Plus Man = .5mr2 + mr2 = (.5)(200)(4) + (30)(4) = 520

w = 2pi/6 = 1.047 rad/s, so...

(520)(1.047) = 400(w)

w = 1.309 rad/s

T = 2pi/w = 2pi/1.309

T = 4.8 sec

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