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Re: kinetic energy erratum

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  • Re: kinetic energy erratum

    I would like to make a clarification on my previous posting about
    rotational kinetic energy. In that posting I gave the following example:

    >For example, a block sliding across a frictionless table has translational
    >kinetic energy ("TKE") because its center of mass is moving, but not
    >rotational kinetic energy ("RKE"). On the other hand, a distributed mass
    >which is rotating about its center of mass, but not moving (such as a
    >bicycle wheel spinning in place) has RKE, but not TKE (because the ceter of
    >mass does not move).

    It was brought to my attention that this example was perhaps not the best,
    in that I suggest that this only holds for rotations about the center of
    mass. However, RKE is generated by any arbitrary rigid body rotating about
    any arbitrary axis of rotation. My example of the bicycle wheel was meant
    to be for the simplified case where this rotation occurs about the center
    of mass. I appologize if there was any confusion on this point.

    However, the more general form of the equation for RKE which I gave at the
    end of my posting does still hold:

    >We can then make similar arguments about RKE, and we derive the following
    >relationship:
    >
    > RKE = (1/2) I * (W*W)
    >
    >where I is the moment of inertia of the rigid body about the instantaneous
    >axis of rotation, and W is the instantaneous angular velocity of the rigid
    >body.

    In this case, I is the moment of inertia about any arbitrary axis, and this
    is typically computed using the parallel axis theorem, such that:

    I' = Icm + M * (d*d)

    where I' is the moment of inertia about the arbitrary axis, Icm is the
    moment of inertia about an axis parallel to I' and passing through the
    center of mass, and d is the Euclidean distance between these two axes.

    I hope this is now clear(er),

    Jon Dingwell

    -------------------------------------------------------------
    Jonathan Dingwell, Ph.D.
    Postdoctoral Research Associate

    Sensory Motor Performance Program
    Rehabilitation Institute of Chicago
    345 East Superior, Room 1406
    Chicago, Illinois, 60611

    Phone: (312) 238-1233 [Office] / (312) 238-1232 [Lab]
    FAX: (312) 908-2208
    E-Mail: j-dingwell@nwu.edu
    Web: http://manip.smpp.nwu.edu/dingwell/
    -------------------------------------------------------------

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