A thin hoop of mass and radius moves across a horizontal surface

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A thin hoop of mass

2.0\,{\rm kg}

and radius

0.30\,{\rm m}

moves across a horizontal surface. The center of mass of the hoop translates at

2.0\,{\rm m\,s^{-1}}

, and at the same time the hoop spins about its central axis at an angular speed of

10\,{\rm rad\,s^{-1}}

. The moment of inertia of a thin hoop about its center is

I = MR^{2}

. (a) Calculate the translational kinetic energy of the hoop. (b) Calculate the rotational kinetic energy of the hoop about its center of mass. (c) Determine the total kinetic energy of the hoop. (d) The same hoop now rolls without slipping while its center of mass maintains a speed of

2.0\,{\rm m\,s^{-1}}

. Calculate the percentage change in its total kinetic energy compared with the situation described in parts (a)–(c).

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