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22 February, 00:06

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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  1. 22 February, 01:27
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    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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