Three objects, A: (a$$ solid $$sphere), B: (a$$ thin circular $$disk) and C: (a$$ circular $$ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

Question

Three objects, A: (a$$ solid $$sphere), B: (a$$ thin circular $$disk) and C: (a$$ circular $$ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

Infinity Learn · Accepted Answer

Work done required to bring a object to restΔ$$W=$$Δ$$KE$$Δ$$W=12I$$ω$$2$$; where $$I=$$ moment of inertia  For same ω,ΔW∝I For a solid sphere, $$IA=25MR2$$ For a thin circular disk, $$IB=12MR2$$ For a circular ring, $$IC=MR2$$∴  IC>IB>IA∴WC>WB>WA

Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $ω$ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

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Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

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Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $ω$ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation