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Re: Conservation of Angular Momentum

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  • Re: Conservation of Angular Momentum

    To Donald Sussman and Biomch-L:

    Let's say that in the initial conditions the person and turntable
    are still and the wheel is rotating counterclockwise (in a view from
    overhead). That means that the combined system (person + turntable + wheel)
    has counterclockwise angular momentum (all of it in the wheel). For
    instance, let's say that this angular momentum is 4 Kgm2/s.

    If the person then flips the wheel upside down, the wheel will now
    be rotating clockwise (in a view from overhead), and therefore it will have
    an angular momentum of -4 Kgm2/s (notice the negative sign, implying
    clockwise rotation!) but the combined system still needs to have the same
    angular momentum as before the flipping of the wheel occurred (i.e., +4
    Kgm2/s). Therefore the person and the turntable will start rotating
    counterclockwise with an angular momentum of +8 Kgm2/s, so that +8 Kgm2/s
    (in the person+turntable) + (-4 Kgm2/s) (in the wheel) = +4 Kgm2/s in the
    combined system.

    All of the above assumes that the connection between the turntable
    and the ground is frictionless, and therefore produces no torque about the
    vertical axis.

    It also assumes that the axle of the wheel is aligned with the axle
    of the turntable. If not, the same basic phenomenon will still occur, but
    the numbers will be somewhat different: If the axle of the wheel is
    off-center relative to the axle of the turntable, the +8 Kgm2/s will be
    "stored" not only in the person and in the turntable, but also partly in the
    wheel itself, because it will produce the counterclockwise rotation of the
    center of mass of the wheel around the vertical axis of the turntable. This
    is usually called the "remote" angular momentum of the wheel (to
    differentiate it from the "local" angular momentum of the wheel, which is
    the -4 Kgm2/s associated with the rotation of the wheel about its own axle).

    There are very good explanations of all this (and of many other
    principles of rotation) in a wonderful book by Bernard Hopper: The Mechanics
    of Human Movement (ISBN 0-444-19550-5). Unfortunately, the book has been
    out of print for many years, but you may find it in your university library
    or through inter-library loan.

    Jesus Dapena
    Jesus Dapena
    Department of Kinesiology
    Indiana University

    Bloomington, IN 47405, USA