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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:

    [tex]I=\frac{2}{5}mr^{2}.[/tex]

    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

    Astronuc

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    Staff: Mentor

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

    http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mi

    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

    Tide

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    Science Advisor
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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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