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Homework Help: New method finding moment of inertia of a soild sphere

  1. Jun 11, 2006 #1
    Q. Show the moment of inertia of sphere is 2/5mR^2
    using many different methods.

    My professor said he knew 18 different method.
    Do you have a new idea?
    Tell me anything you know. I hope one of your methods will be the 19th method.
     
  2. jcsd
  3. Jun 11, 2006 #2
    The inertia for a point mass is [tex]I = mr^{2}[/tex]. If you have a sphere you can treat it as a large number of point masses and add them together as in [tex]I = \sum m_{i}r_{i}^{2}[/tex]. It is probably better to solve this using calculus though. For rotational inertia the equation [tex]I = \sum m_{i}r_{i}^{2}[/tex] is an approximation of [tex] I = \int r^{2} dm [/tex].

    Rotational inertia is also related to kinetic energy. Kinetic energy can be expresses as [tex]K = \frac{1}{2} I \omega^{2}[/tex] where [tex]\omega[/tex] is the angular speed.

    I've never heard anyone say that there 18 ways to solve this problem, but I suppose it might depend on what other information you might be given.

    hope that helps

    -dim
     
    Last edited: Jun 11, 2006
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