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What is wrong with my derivation for the moment of inertia of a sphere?

  1. Mar 20, 2010 #1
    Ok, so I thought about a derivation for the moment of inertia, but my answer comes out to (3/5)MR^2

    Basically, what I did was I considered the sphere as a sum of infinitesimally thin spherical shells.

    The moment of inertia for one shell is dI=(r^2)*dm

    where dm=(M/V)*4*pi*r^2*dr

    where V=(4/3)*pi*R^3

    so the equation dI=3*pi*M*r^4*dr when simplified.

    Integrating this from 0 to R (Summing up the spherical shells from the center to the edge of the big sphere) gives me (3/5)*M*R^2. The process clearly yields the wrong answer, so I need help seeing where the fault is.
  2. jcsd
  3. Mar 20, 2010 #2


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    Homework Helper

    The moment of inertia of a thin shell is (2/3)MR^2, not MR^2, so your original dI should be (2/3)r^2 dm - there's your missing factor of 2/3.
  4. Mar 20, 2010 #3
    Ohhhhh, I see. I was treating it as a point.
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