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Homework Help: Moments of Inertia

  1. Nov 16, 2005 #1
    Could someone direct me to a site that explains how the common moments of inertia were arrived at? My physics professor put up on the board today that for a uniform sphere:


    He said it was just the anti-derivative of something, but he didn't want to go into it because there is a table in our book with all of the common moments of inertia.

    Does anyone know? Maybe someone could show me how the above moment (for the sphere) was derived and I could try it on something else? Thanks, I'd appreciate it.
  2. jcsd
  3. Nov 16, 2005 #2


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    The general form of the moment of inertia involves an integral of the mass distribution and moments of the mass.


    The fourth and fifth plates provide an example of the integration ('anti-derivative') used to determine the moment of inertia.

    Think about how a center of mass is defined.
  4. Nov 16, 2005 #3


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    You need to integrate [tex]r^2 \sin^2 \theta[/tex] over the volume of the sphere. Note that this represents the square of the perpendicular distance of a point in the sphere from the axis of rotation. Also, note that [tex]dV = r^2 dr d\phi \sin \theta d\theta[/tex].
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