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Moment of inertia of spherical shell

  1. Jan 29, 2006 #1

    i have to give a presentation on an example of the defining equation for the moment of inertia of a thin spherical shell. I have to follow the example in my book "elements of newtonian mechanics". I get most of it but there are a couple steps that the book skips that i cannot. I was wondering if anyone could better explain whats happening to me.

    There is a thin spherical shell of mass M and radius R which is symetrically identical in the x, y and z coordinate system.

    Ix = Iy = Iz

    now Ix = integral (y^2 + z^2)dM i dont get this step.

    R^2 = x^2 but i dont get the geometry of why x^2 = y^2 + z^2

    Iy = integral (z^2 + x ^2)dM etc

    now it says Itotal = 1/3(Ix + Iy + iz)

    where does the 1/3 come from. Is it just taking the average or does it have to do with the parrallel axis theorem?
  2. jcsd
  3. Jan 29, 2006 #2


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    Homework Helper

    I'm not sure if you have figures in your text, but I can't see them.

    Supposing I understood the situation correctly, the answer to your problem(s) would be the Pythagorean theorem.
  4. Jan 29, 2006 #3
    yeah i understand that now. I still dont get why the total inertia is 1/3(Ix + Iy + iz) though
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