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Moment of inertia of a solid sphere

  1. Feb 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the moment of inertia of a solid sphere of uniform mass density (like a billiard ball) about an axis through its center

    2. Relevant equations
    I = ∫rρdV

    3. The attempt at a solution
    I =ρ ∫r4πr2dr = ρ4π∫r4
    Then I integrate this from 0 (the center) to R, so I = (ρ4π)*(R5/5)
    And ρ = mv so ρ = M/(4/3)πR3 = 3M/4πR3. Put ρ into the equation for moment of inertia to get I = 3MR2/5.

    My book tells me the answer is (2/5)MR^2. Where did I go wrong?
     
  2. jcsd
  3. Feb 14, 2015 #2

    PeroK

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    Can you explain how you are setting up the integral? What shape are you integrating from 0 to R?
     
  4. Feb 14, 2015 #3
    The surface area of a spherical shell from the center of the sphere to the outer shell of radius R.
     
  5. Feb 14, 2015 #4
    I figured it out. If I use spherical shells, the points from the shell aren't all the same distance form the axis of rotation. I was thinking about the distance from the center.
     
  6. Feb 14, 2015 #5

    PeroK

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    Exactly!
     
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