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19 May, 07:36

A hoop with mass m and radius R is rolling without slipping on a horizontal surface with its center moving at a speed v. The rotational inertia of the hoop about its center is mR2. What is its total kinetic energy

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  1. 19 May, 09:24
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    K. E. (Total) = 1/2 m (v² + R² ω²)

    Explanation:

    K. E. (Total) = Translation K. E. + Rotational K. E.

    K. E. (Total) = 1/2 mv² + 1/2 I ω²

    K. E. (Total) = 1/2 mv² + 1/2 I ω² (I = m R² given)

    K. E. (Total) = 1/2 mv² + 1/2 m R² ω²

    K. E. (Total) = 1/2 m (v² + R² ω²)
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