Re: Center-of-mass system

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

>         I checked over an exam question written by a younger
> colleague, who used
> the term "center-of-momentum system."  I objected, saying it could be
> "center-of-mass system" or "zero-momentum system" but not
> "center-of-momentum system,"  which sounds nonsensical to me.
>         Checking with other faculty I found two other young faculty who liked
> "center-of-momentum system" and preferred it, telling me it was common, and
> two older faculty who considered it an abomination and only really liked
> "center-of-mass system."  All four of these faculty are researchers more
> than teachers in their interests.
>         Comments?
>
> Laurent Hodges, Professor of Physics
> 12 Physics Hall, Iowa State University, Ames, IA  50011-3160
> lhodges@iastate.edu   http://www.public.iastate.edu/~lhodges

I vote for "center of mass." I don't see much meaning in the phrase
"center of momentum." We have a perfectly good definition of center
of mass in terms of the weighted average of the position of all the
individual masses in the system. This definition has nothing to do
with motion. Then once we have found the center of mass, we can *use*
it as a point that moves *as if* all the mass were concentrated at
that point. And if we happen to be sitting on that point, or at least
not moving relative to it, then it happens that the momentum of all
of the system is zero, as we see it. But that is true whether or not
we are at the center of mass or not, just as long as our motion is
the same as the motion of the center of mass, thus we are in a frame
of reference in which the center of mass is at rest--the "center of
mass" reference frame.

I have always found it useful to define a reference frame in terms of
something that was at rest in that frame, in other words, some
physical (or defined in terms of physical) object(s). Momentum is a
construct that we find very useful, but it is not a physical object
like a mass, and so I do not feel comfortable calling a reference
frame by that name, because there is no place I can point to and say
"There. That is the point that this coordinate system is referenced
to." Since the point that the frame we are talking about is
referenced to is the center of mass, that is what we should call it.

Hugh
--

Hugh Haskell
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
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