A playground carousel is free to rotateabout its center on frictionless bearings

Question

A playground carousel is free to rotateabout its center on frictionless bearings, and air resistance isnegligible. The carousel itself (without riders) has a moment ofinertia of 120kg·m2. When one person is standing at a distanceof 1.50 m from the center, the carousel has an angular velocity of0.700 rad/s. However, as this personmoves inward to a point located 0.750 m from the center, theangular velocity increases to 0.850rad/s. What is the person's mass?
1 kg

A playground carousel is free to rotateabout its center on frictionless bearings, and air resistance isnegligible. The carousel itself (without riders) has a moment ofinertia of 120kg·m2. When one person is standing at a distanceof 1.50 m from the center, the carousel has an angular velocity of0.700 rad/s. However, as this personmoves inward to a point located 0.750 m from the center, theangular velocity increases to 0.850rad/s. What is the person's mass?
1 kg

Explanation / Answer

Angular momentum conservation: Iii =Iff (Io + mri2)i =(Io +mrf2)f Ioi+ mri2i =Iof +mrf2fm(ri2i -rf2f) =Io(f - i)                  m = Io(f - i)/(ri2i -rf2f) = 16.41 kg

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