Rolling

AP Physics 1· difficulty 4/5

hoop sphere

A solid sphere (I=25MR2I = \tfrac{2}{5}MR^2) and a hoop (I=MR2I = MR^2) are released from rest at the same height on an incline and roll without slipping. Which reaches the bottom first?

  • A

    They tie because mass cancels

  • B

    Sphere; its acceleration is 57gsinθ\tfrac{5}{7}g\sin\theta vs hoop 12gsinθ\tfrac{1}{2}g\sin\theta

    check_circle
  • C

    Hoop; lower moment of inertia

  • D

    Sphere only if it is heavier

Explanation

Acceleration on incline is a=gsinθ/(1+I/MR2)a = g\sin\theta/(1 + I/MR^2). Sphere: a=57gsinθa = \tfrac{5}{7}g\sin\theta; hoop: a=12gsinθa = \tfrac{1}{2}g\sin\theta. Sphere wins.

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