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

Explanation / Answer

I = 125 kg.m^2, w1 =0.6 rad/s, d1 =1.5 m,d2 =0.93 m , w2 =0.8 rad/s

Mass of person m = ?

From conservation of angular momentum

I1w1 =I2w2

[I +md1^2]w1 = [I+md2^2]w2

[125+ (m*1.5*1.5)]0.6 =[125+ (m*0.93*0.93)]0.8

Mass of person m =37.99 kg

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