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

Explanation / Answer

total angular momentum is conserved

so

125*0.6 + m*1.5^2*0.6 = 125*0.8 + m*1.04^2*0.8

0.49*m = 25

so m = 51 kg

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