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Total angular momentum Q

  1. Dec 21, 2005 #1
    hey everyone, I've been working through a past paper and I'm stuck on a question:

    "(a) Consider a system consisting of n distinct particles P1, P2, : : :, Pn, with masses m1, m2, ...., mn and position vectors r1, r2, : : :, rn, relative to the origin O of an inertial frame, respectively.

    For each i = 1, 2, : : :, n, suppose that the only forces acting on Pi are internal forces Fij , which always act along the line joining Pi and Pj , for j = 1, 2, : : :, n and j doesn't equal i.

    Assume that Fij = ¡Fji for i = 1, 2, : : :, n, j = 1, 2, : : :, n and i doesn't equal j.

    Define what is meant by the total angular momentum of the system about O.

    Show, as a consequence of Newton's second law, that the total angular momentum of the system about O is constant."

    I can define the total angular momentum of the system, it's the 2nd part of the Q I have trouble with. :confused:

    Thanks
     
  2. jcsd
  3. Dec 21, 2005 #2

    Tide

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    Use the defintion of angular momentum:

    [tex]\vec L = \vec r \times \vec p[/tex]

    Take the time derivative and sum over all particles noting that

    [tex]\frac {d \vec p}{dt} = \vec F[/tex]

    You will find [itex]d\vec L /dt = 0[/itex].
     
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