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 115 kg·m2. When one person is standing at a distance of 1.74 m from the center, the carousel has an angular velocity of 0.517 rad/s. However, as this person moves inward to a point located 0.791 m from the center, the angular velocity increases to 0.724 rad/s. What is the person's mass?

Explanation / Answer

Given Data

J = 115 kg·m2
Mass of person: m
Initial radius: R1 = 1.74 m
Final radius: R2 = 0.791 m
Initial angular velocity: w0 = 0.517 rad/s
Final angular velocity: w1 = 0.724 rad/s.

Solution:-

Initially, the angular momentum is thus:
L = (J + m*R1^2)*w0

Finally, it is:
L = (J + m*R2^2)*w1

m = J*(w1 - w0)/(w0*R1^2 - w1*R2^2)

= 115 * (0.724 - 0.517) / (0.517 * 1.74^2 - 0.724 * 0.791^2)

    = 21.4 kg

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