A playground carousel is free to rotate about its center on frictionless bearing

Question

A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 125 kg · m2. When one person is standing on the carousel at a distance of 1.5 m from the center, the carousel has an angular velocity of 0.6 rad/s. However, as this person moves inward to a point located 0.915 m from the center, the angular velocity increases to 0.8 rad/s. What is the person's mass?

Explanation / Answer

Hints: Given that Ic = 125 kg.m^2 rc = 1.5 m wo = 0.6 rad/s rp = 0.915 m wf = 0.8 rad/s According to conservation of angular momentum we have Ic wo + Ipo wo = Ic wf + Ipf wf ==> Ic wo + (m ro^2) wo = Ic wf + (m rp^2) wf ==> m = Ic (wf - wc) / (ro^2 * wo - rf^2 * wf) Substitute values and solve for mass m.

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