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Moments of Inertia of a Flat Body

  1. Mar 26, 2009 #1
    How do you take the moments of inertia of a flat body? I know howto take it if it's a 3d body. And the 2d case should be really simpe,but I'm too stupid to figure it out. Can you help me? For example.. Say we have a body that's a rectangle of mass m on |x| < a, |y| < b..? Thanks so much.
     
    Last edited: Mar 26, 2009
  2. jcsd
  3. Mar 26, 2009 #2

    tiny-tim

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    Hi hamjam9! :smile:

    I assume you're given a mass-per-area instead of a density?

    For a "flat" body (no such thing, really :rolleyes:), you just treat it as if it has a very very small thickness. :wink:
     
  4. Mar 26, 2009 #3
    Or perhaps the thickness doesn't matter. Could it be unit thickness? As long as the density doesn't vary with the z-coordinate of your example.

    In any case, I usually find it easier to do a double integral [tex]\int \int r^2 \sigma(x,y) dx dy[/tex] than a triple integral [tex]\int \int \int r^2 \sigma(x,y,z) dx dy dz[/tex]
     
  5. Mar 27, 2009 #4

    tiny-tim

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    Hi hamjam9! :smile:

    No, none of the moments of inertia is zero.

    Look at the PF library on moment of inertia :wink:

    Any axis of symmetry is a principal axis.

    Any body has a different moment of inertia about every axis …

    this question asks you for the ones about the principal axes. :smile:
     
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