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 125 kg·m2. When one person is standing on the carousel at a distance of 1.50 m from the center, the carousel has an angular velocity of 0.600 rad/s. However, as this person moves inward to a point located 0.795 m from the center, the angular velocity increases to 0.800 rad/s. What is the person’s mass?

Explanation / Answer

moment of inertia of carousel , I1 = 125 Kg.m^2

let the mass of person is m

Now, as there is no external torque acting on the wheel ,

using conseravtion of angular momentum

Ii * wi = If * wf

(125 + m * 1.50^2) * 0.6 = (125 + m * 0.795^2) * 0.8

solving for m

m = 29.6 Kg

the mass of person is 29.6 Kg

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