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Moment of inertia help me please

  1. Feb 20, 2004 #1
    I'm don't really know how to find the momemt of inertia. I have two questions that I'm stuck on.

    Two questions:

    1. Find the moment of inertia of a sheet f mass M and uniform density which is in the shape of a rectangle of sides a and b, for rotations about an axis passing through its center and perpendicular to the sheet.

    answer:Will I start with this I= (integral over A)M/A dA? How would I find the limits of integration and integrate this?

    2. Find the moment of inertia of a thin uniform disk of mass M and radius a for rotations about an axis through a diameter of the disk.

    answer: Will th answer be I=2M/a^2 (a^4/4)=Ma^2/2?
     
  2. jcsd
  3. Feb 20, 2004 #2

    matt grime

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    1. that isn't the answer, no

    I is the integral over A of pr^2 dA where p is the density and r is the distance from the origin


    ie int over A of p(x^2+y^2)dxdy

    the limits for x are -a/2 to a/2 and y is -b/2 to b/2

    also use abp=M, I'm presuming you can do double integrals - this one is quite easy.

    the second one is somewhat harder, but just try this for now.
     
  4. Feb 20, 2004 #3
    is this right

    M(a^2/48+b^2/48) is the moment of inertia
     
  5. Feb 20, 2004 #4

    matt grime

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    you're about a factor of 16 out, how did you get that? show your working...
     
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