Re: How atrocious is "center of gravity"?

[Leigh Palmer <palmer@SFU.CA>]

You neglected to mention that as the stick oscillates its center of
gravity, as you have defined it, moves within the body with respect
to the center of mass. In what way is this center of gravity useful?
Can I not calculate the torque about the center of mass without
resorting to use of the center of gravity? Don't I need to calculate
the torque anyway to find the center of gravity? In the vertical
position the position of your weight-weighted center of gravity is
extremal, that's all. Why does one need a special term to pertain to
that point?

You have merely given a way to parameterize the tidal interaction
here. There is no significant utility to the concept of center of
gravity.

Leigh

>        "Center of mass" is a mass-weighted average position. "Center of
> gravity" is a gravitational force-weighted average position (I could have
> said "weight-weighted"). If  g  is essentially constant over the system,
> the center of gravity is essentially at the center of mass. Then we can do
> without the term "center of gravity".
>        However, here's an example where both terms are useful. Suppose a
> meter stick is in orbit about the earth. If the stick is NOT horizontal,
> particles of the stick closer to the earth have a bit more gravitational
> force than equal-mass particles farther from the earth. As a result, the
> center of gravity is below the center of mass. Since we can treat the
> entire weight of the stick as acting at its center of gravity, the weight
> of the stick exerts a torque about the stick's center of mass, tending to
> align the stick's long axis with the earth's gravitational field.
>        This torque can be used to orient satellites (my memory is that
> the jargon is something like gravitational-gradient orientation). Allowed
> to swing freely, the stick will oscillate back and forth about its
> alignment position. It's not hard to get a good approximation for its
> period using centers of gravity--I did so many years back when the AAPT
> was looking for experiments to be done in orbit.
>                                                        Tom Sandin
>
>
> On Thu, 13 Apr 2000, Leigh Palmer wrote:
>
> > Of greatest importance is that one should *never* allow the use of
> > "center of gravity"! There is no case where this atrocious construct
> > is more appropriate than "center of mass".
> >
> > Leigh