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Moment of inertia of solid sphere

  1. Nov 17, 2009 #1
    Hi, i am trying to find the moment of inertia of a uniform density solid sphere about z-axis

    I = integrate => x^2 dm

    x = perpendicular distance from z-axis to anywhere in sphere
    so by pythagorus theorem, r^2 - z^2 = x^2

    since dm = p dV
    and V = 4/3 (//pi)r^3
    dV = 4(//pi)r^2 dr

    so I = integrate=> r^2 - z^2 pdV

    but the problem is z is a variable.

    so how do i convert z?

    assuming i put z = rcos θ,

    then i will have a θ variable now.

    i tried integrating θ from 0 to (pi) but the answer is wrong, its not 2/5mr^2

    so what should i do?

    thanks
     
  2. jcsd
  3. Nov 17, 2009 #2

    Vanadium 50

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    Look at your volume element.
     
  4. Nov 17, 2009 #3
  5. Nov 17, 2009 #4
    i have seened that, but they considered slices of circular disk

    and so they sum up the moment of inertia of each disk for the whole sphere

    but i am sure the method that i am doing can work also.. just that i don't know how
     
  6. Nov 17, 2009 #5
    whats wrong with the volume element?
     
  7. Nov 17, 2009 #6
    If you are not summing slices, what are you summing in your integration? I suppose maybe you could take ever-widening, and ever-shortening cylinders centered about an axis. The first piece would be a line, and the last would be a circle. Is that what you are doing?
     
    Last edited: Nov 17, 2009
  8. Nov 18, 2009 #7
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