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Moment of inertia question.

  1. Jan 3, 2013 #1
    Hi,
    1. The problem statement, all variables and given/known data
    Will the moment of inertia of a two dimensional rectangle (with sides a, b) whose axis is parallel to one of its sides and passes through its center of mass, be (1/12)M(a2+b2)?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 3, 2013 #2

    haruspex

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    No. If the axis is, say, the y axis, think of the lamina as a set of parallel thin strips in the x direction. They'll all have the same moment. I think the formula you quoted would be right for an axis perpendicular to the lamina.
     
  4. Jan 3, 2013 #3
    But then wouldn't I be getting a moment of inertia equal to (Ma^2)/12 (supposing axis is parallel to a)?
     
  5. Jan 3, 2013 #4

    haruspex

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    And what's wrong with that?
     
  6. Jan 3, 2013 #5
    It's not that something's wrong with that, simply that it seemed a bit strange it would not depend on the other side too.
     
  7. Jan 3, 2013 #6

    haruspex

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    That's why I said to think of it as parallel strips across the axis. Adding more only increases the moment in proportion to the mass.
     
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