1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook