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Moment inertia - theoretical problem

  1. Sep 4, 2013 #1
    Moment inertia -- theoretical problem

    1. The problem statement, all variables and given/known data

    Show that the moment inertia of a hollow cylinder with inner radius a and outer radius b is (1/2)*M*(a^2+b^2), calculated for the center axis.

    2. Relevant equations

    I know that the moment inertia of a non-hollow cylinder is I = (1/2) MR^2, but I don't know the moment inertia of a hollow one.

    I = MR^2, generally.

    Krotation = (1/2)Iw^2

    3. The attempt at a solution

    I'm not entirely certain on where to start. Should I split the cylinder into two parts and work from there?
     
  2. jcsd
  3. Sep 4, 2013 #2

    Doc Al

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    Staff: Mentor

    Yes. Consider overlapping cylinders. Subtract!

    Be careful with the mass.
     
  4. Sep 4, 2013 #3
    I'm sorry but I'm still having problems... I googled the problem and all of the solutions use definite integration. Can I solve this problem without using that?
     
  5. Sep 4, 2013 #4

    Doc Al

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    Staff: Mentor

    All you need to know is the formula for the moment of inertia of a solid cylinder--which you already know.

    Hint: For a composite body with parts a and b, Itotal = Ia + Ib.
     
  6. Sep 4, 2013 #5
    Sorry for the late reply. I did it!! :D Thanks a lot.
     
  7. Sep 5, 2013 #6

    Doc Al

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    Staff: Mentor

    :thumbs:
     
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