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Homework Help: Total energy of a rolling sphere

  1. Nov 16, 2008 #1
    1. The problem statement, all variables and given/known data
    A solid sphere has a mass of 1.0 kg. It is rolling at a translational speed of 10 m/s. What is the total energy of the rolling sphere?
    I think I got the problem but I'm not sure I went about it the right way.

    2. Relevant equations
    I = (2/5)mr^2
    KE_rot = (1/2)Iw^2
    KE = (1/2)mv^2

    3. The attempt at a solution
    I assumed KE_total = KE_rot + KE...which I'm not sure is right.
    KE_rot = (1/2)Iw^2 = (1/2)(2/5)(m)(r^2)(w^2) = 20 Joules
    KE = (1/2)(m)(v^2) = 50 Joules

    KE_total = 70 Joules
    This is the right answer, but I'm not sure if the total kinetic energy is actually the rotational kinetic energy plus the linear kinetic energy. Also...what is translational velocity? Is this any different than the sphere moving in a direction?
  2. jcsd
  3. Nov 16, 2008 #2


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    Homework Helper

    That's right.

    The translational velocity is the velocity of the center of mass.

    The rotational energy is about an axis through the center of mass.
  4. Nov 16, 2008 #3


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    Homework Helper

    Here is a link that touches on rolling motion if you are interested in further study:
    http://dept.physics.upenn.edu/courses/gladney/mathphys/java/sect4/subsubsection4_1_4_3.html [Broken]

    (Page down to rolling motion section.)
    Last edited by a moderator: May 3, 2017
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