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Moment of inertia with varying density

  1. Apr 20, 2007 #1
    I had to find the moment of inertia of a sphere of varying density where the density is some constant times the radius.

    I used the equations from here


    I inserted this d=cr in for the density.

    For the mass I used dm=4(pi)(d)r^2dr, inserted the density, integrated and solved for c.

    After substitution I the answer I got was 2/15mr^2.

    Does this sound right?
  2. jcsd
  3. Apr 21, 2007 #2


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    Gold Member

    The answer should be between the solid sphere value and the thin shell value, so your answer is too small. I did a rough calculation and got 1/2Mr^2.

    Can you show more of your working ?
  4. Apr 21, 2007 #3


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    Homework Helper

    your dm element seems ok if you are taking thin shell as your differential element. I got [tex]\frac{4}{9} MR^2[/tex]. you should check whether you have got constant c correct.
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