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Homework Help: Moment of inertia of an irregularly shaped object

  1. Feb 24, 2005 #1
    This problem describes one experimental method of determining the moment of inertia of an irregularly shaped objectt such as the payload for a satelite. http://home.earthlink.net/~suburban-xrisis/clip2.jpg [Broken] shows a mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. When the mass is released from rest, it descends through a distance h, acquiring a speed v. Show that the moment of inertia I of the equptment (including the turntable) is [tex]mr^2(2gh/v^2-1)[/tex].

    here's what I tried, by using this fromula I found in the book:






    I'm not sure how to get the right answer.
    Last edited by a moderator: May 1, 2017
  2. jcsd
  3. Feb 24, 2005 #2
    Divide each of the terms in the bracket by v^2.
  4. Feb 24, 2005 #3






    This does not equal

    what did I do wrong?
  5. Feb 24, 2005 #4

    [tex]I=mr^2 * \frac{2gh-v^2}{v^2}[/tex]

    [tex]\frac{2gh-v^2}{v^2} = \frac{2gh}{v^2} - 1[/tex]

    [tex]I=mr^2(\frac{2gh}{v^2} - 1)[/tex]
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