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Consider a uniform solid sphere of radius R and mass M rolling without slipping. The moment of inertia of the sphere about an axis through its center is 25MR2. Which form of its kinetic energy is larger, translational or rotational? Consider

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MathPhys

Explanation:

Its translational kinetic energy is:

KE = ½ mv²

It's rotational kinetic energy is:

RE = ½ Iω²

For a solid sphere, I = ⅖ mr², and since it's not slipping, ω = v/r.

RE = ½ (⅖ mr²) (v/r)²

RE = ⅕ mv²

Therefore, the translational kinetic energy is larger.

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