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

initial Ii = 125 + (m * 1.52)

If = 125 + (m * 1.082)

From conservation of angular momentum

[125 + (m * 1.082)]* 0.8 = [125 + (m * 1.52)] * 0.6

125 + 1.17 m = [125 + 2.25 m] * [0.6/0.8]

125 + 1.17 m = 93.75 + 1.69 m

person's mass m = 60 kg

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