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Homework Help: Moment of inertia

  1. Feb 19, 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 19, 2004 #2
    Start with:

    [tex] \int r^2 dm = \int r^2 \sigma dA = \sigma \int r^2 dA [/tex]

    Where [itex] \sigma [/itex] is the constant density [itex] \frac{M}{A} [/itex]

    hope that helps
     
  4. Feb 20, 2004 #3
    dnn't understand

    could someone explain itto me?
     
  5. Feb 20, 2004 #4
    Re: Re: moment of inertia

    [tex]\sigma \int r^2 dA =\sigma \int (x^2+y^2)dxdy [/tex]

    this is ok since if you draw the rectangle out, r is measured from the center of the plane and therefore [itex] r^2=x^2+y^2 [/itex]. Since the center of the plane is the axis of rotation... you should be able to figure out the limits of integration for x and y.
    Cheers.
     
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