Conceptual Example 14 provides useful background for this problem. A playground

Question

Conceptual Example 14 provides useful background for this problem. 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 0.993 m from the center, the angular velocity increases to 0.8 rad/s. What is the person's mass?

Explanation / Answer

here angular momentum remain conserve

Li = Lf

Ic*wi + Ip*wi = Icwf + Ip*wf

Ip = mr^2

mri^2*wi + Ic*wi = m*rf^2*wf + Ic*wf

Ic(wf-wo) = m(ri^2wi - rf^2*wf)

m = Ic(wf-wo) / (ri^2wi - rf^2*wf)

m = 44.55 kg

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