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 124 kg-m^. When one person is standing at a distance of 1.64 m from the center, the carousel has an angular velocity of 0.557 rad/s. However, as this person moves Inward to a point located 0.651 m from the center, the angular velocity increases to 0.717 rad/s. What Is the person's mass?

Explanation / Answer

Let the person's mass = m

Moment of inertia of system when the person is at distance r = 124 + mr^2

I1 = 124+m*1.64^2 = 124+2.69m

I2 = 124+0.424m

By conservation of angular momentum,

I1w1 = I2w2

(124+2.69m)*0.557 = (124+0.424m)*0.717

m = 16.61 kg

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