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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

1. Wₐ > Wᵦ > W꜀
2. Wᵦ > Wₐ > W꜀
3. Wₐ > W꜀ > Wᵦ
4. Wᵦ > W꜀ > Wₐ

Correct answer: Wₐ > Wᵦ > W꜀

Solution

The work required to bring a rotating object to rest is equal to its rotational kinetic energy, which is given by (1/2)Iω², where I is the moment of inertia. For the same mass and radius, the moments of inertia are Iₐ = (2/5)MR² for the solid sphere, Iᵦ = (1/2)MR² for the disk, and I꜀ = MR² for the ring. Since I꜀ > Iᵦ > Iₐ, the work required satisfies Wₐ > Wᵦ > W꜀.

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