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Rotational Kinetic Energy

AP Physics 1· difficulty 4/5

v hoop, M, R

A thin hoop (I=MR2I = MR^2) rolls without slipping on a level surface with center-of-mass speed vv. What fraction of its total kinetic energy is rotational?

  • A

    2/52/5

  • B

    2/72/7

  • C

    1/21/2

    check_circle
  • D

    1/31/3

Explanation

Ktrans=12Mv2K_{trans} = \tfrac{1}{2}Mv^2 and Krot=12(MR2)(v/R)2=12Mv2K_{rot} = \tfrac{1}{2}(MR^2)(v/R)^2 = \tfrac{1}{2}Mv^2. So Krot/Ktot=1/2K_{rot}/K_{tot} = 1/2.

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