Rolling

AP Physics 1· difficulty 3/5

A solid sphere, a solid disk, and a thin hoop — same mass and radius — are released simultaneously from rest at the top of a ramp and roll down without slipping. Which reaches the bottom <strong>first</strong>?

  • A

    The thin hoop

  • B

    The solid sphere

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  • C

    They all tie.

  • D

    The solid disk

Explanation

The smaller the factor in I=kMR2I = kMR^2, the greater the fraction of PE that becomes translational KE. ksphere=2/5<kdisk=1/2<khoop=1k_{\text{sphere}} = 2/5 < k_{\text{disk}} = 1/2 < k_{\text{hoop}} = 1. The sphere wins.

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