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Violating the law of conservation of energy

  1. Feb 24, 2013 #1
    I know that's impossible, so please help me!!!

    Let there be a body rotating about its axis, with a moment of inertia I and an angular velcity w.
    The angular momentum of the system is L = Iw.
    Now, if the radius of the body change, its moment of inertia will also change. Let the new moment of inertia be I`, such that, I`= kI.
    But the angular momentum of the system will remain constant.
    So, the angular velcity must change. So, w`=w/k.
    But, initially, the energy of the system was purely kinetic and was given by
    E=1/2 Iw2.
    The new energy is given by, I`= 1/2 I`w`2 = 1/2 kI (w/k)2
    So, E`= E/k.

    So the new energy of the system is either more {0<k<1} of less {k>1} than the previous energy!

    What am I doing wrong?
  2. jcsd
  3. Feb 24, 2013 #2
    You need to do work to change the radius. Imagine whirling a ball on a string around. If takes work to pull in the ball.
  4. Feb 24, 2013 #3
    ok...got it... so silly of me to even ask this.
  5. Feb 26, 2013 #4


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    The only silly question is the one you don't ask.
  6. Feb 26, 2013 #5
    hmm... who said that?
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