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Rotational and Kinetic Energy - Down a Hill

  1. Apr 4, 2012 #1
    1. The problem statement, all variables and given/known data

    15. Three objects with the same total mass and radius, a hoop, a disk, and a sphere each
    roll without slipping down an incline. Which of the following statements is FALSE?

    A) The hoop has the largest moment of inertia, so it arrives at the bottom first.
    B) The object with the largest rotational kinetic energy has the smallest translational
    kinetic energy.
    C) Each of the objects has the same total kinetic energy at the bottom of the incline.
    D) Total energy is conserved in each case.

    2. Relevant equations

    Hoop: I = Mr^2
    Sphrere: I = (2/5)Mr^2
    Disk: I = (1/2)Mr^2

    3. The attempt at a solution

    K.E. tot = Rotational + kinetic
    K.E. tot (hoop for example) = 1/2 Iω^2 + 1/2 mv^2

    Hmm. Energy is always conserved, so I want to say that makes "C" true too. I'm unsure about "A" and "B."
  2. jcsd
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