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Questioning the law of conservation of mechanical energy

  1. Feb 21, 2012 #1
    I found something interesting in the law of conservation of mechanical energy related with rotational kinetic energy. The law states that:
    ME = KE(translational) + KE(rotational) + PE

    *ME = Mechanical Energy
    *KE = Kinetic Energy
    *PE = Potential Energy

    It was stated that the above law (conservation of ME) can be applied only if there was no external force (such as from friction). However, we also believe that the KE(rotational) exist because of friction (which is an external force).

    So, are we contradicting ourselves? If we apply the above law, then there shouldn't be external force (friction). No friction means no KE(rotational). On the other hand, if we apply KE(rotational) law, then there exist the friction force. If friction occurs, then the above law can't be applied.
  2. jcsd
  3. Feb 21, 2012 #2


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    Any object spinning in space will have no friction but still rotational KE.
  4. Feb 21, 2012 #3
    How if the object is spinning on earth, where the gravitational acceleration (g) still exist? The ME I'm talking about consist of PE=mgh, where g still exist. If the object is on space, where g doesn't exist, then the law doesn't apply anymore.. It's a different case..
  5. Feb 21, 2012 #4


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    Gravitational acceleration can exists in space too. And on Earth, an object free falling in a vacuum tube will experience no friction, but still can have rotational KE. Rotational KE has nothing to do with friction.
  6. Feb 21, 2012 #5
    It's possible to have mechanical energy conservation even if there are external non-conservative forces (friction force is an example of such a force): The work done by those forces just have to be 0. I'm assuming you're referring to the example of a rolling ball? In that case the work of the friction force is 0, because the point where the friction force is exerted doesn't have velocity.

    And what you said is not general at all, that's only a restrict example where the rotation happens because of a friction force.
  7. Feb 21, 2012 #6
    Of course not. If there were no rotational energy, giving the slightest 'tap' to that object from the direction to which it is spinning (which it can't, when it has no rotational energy) would send it spinning the other way around.
  8. Feb 29, 2012 #7
    Thanks for your responses.
    But, how if the case is like this (attachment - rolling the ball).
    Then surely, the point where the friction force is exerted do have velocity. It move downward and experience the gravitational acceleration.. I still don't get it..

    Attached Files:

    Last edited: Feb 29, 2012
  9. Feb 29, 2012 #8
    The term PE in the law appears due to conservative forces such as gravity, Electric field, etc. With a non-conservative force, mechanical energy is not conserved.

    Friction force is non-conservative, however, the force you are talking about is not friction! ( it does not depend on coefficient of friction).

    Imagine a gear ( or a ring) with very fine teeth is rolling down on a surface with teeth of the same size . Due to the weight of the ring, a force is applied on the teeth and the tooth and according to Newton's third law, there is a reaction to the force. Since gravitational force is conservative, this force is conservative too and mechanical energy is conserved with some changes in PE.
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