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

Explanation / Answer

Using law of conservation of angular momentum

I1*w1 = I2*w2

I1 is the moment of inertia of the system when the person is at 1.5 m

I2 is the moment of inertia of the system when the person is at 1.03 m

I1*w1 = I2*w2

(125+(mp*r1^2))*0.6 = (125+(mp*r2^2))*0.8

(125+(mp*1.5^2))*0.6 = (125+(mp*1.03^2))*0.8

mp = 49.87 Kg

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