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Moment of Inertia of Half a Sphere

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data
    a4iUd.png


    2. Relevant equations
    I_a = I_G + md^2


    3. The attempt at a solution
    I tried using the parallel axis theorem to find the moment of inertia about the axis.

    In the formula sheet they give the moment of inertia of a hemisphere:
    I_G = 0.259mr^2, where d, the distance from the center is equal to (3r/8).

    Thus to find the inertia about the axis we will have to solve
    I_a = 0.259mr^2 + m(3r/8)^2

    This ends up giving me 2mr^2/5 which is not the answer... However I still think this is the correct answer. This is because I_a = mr^2/5 = 0.2mr^2 (which is the answer according to the prof) is less than the moment at the center I_G = 0.259mr^2. According to the parallel axis equation I_a = I_G + md^2, I_a must be larger than I_G not smaller...
     
  2. jcsd
  3. Oct 24, 2012 #2

    ehild

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    Homework Helper
    Gold Member

    Go back to the definition of the moment of inertia. What is the moment of inertia of a point mass, at distance R from the rotation axis? What if you have two identical point masses at the opposite ends of a diameter?

    Your problem is connected to "m". What is it?

    ehild
     
    Last edited: Oct 24, 2012
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