Conceptual Example 13 provides useful background for this problem. A playground

Question

Conceptual Example 13 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 1.08 m from the center, the angular velocity increases to 0.8 rad/s. What is the person's mass?

Explanation / Answer

Itotal = Ic + Ip

Ic = moment of inertia of carousel

Ip = inertia of person

initially

Itotal = 125 + m(1.5)^2

final = 125 + m(1.08)^2

here angular momentum is conserve

Ii*w1 = If*w2

=(125 + m(1.5)^2)*0.6 = [125 + m(1.08)^2]*0.8

75 + 1.35m = 100 + 0.93312m

m = 59.97 kg = 60 kg

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