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Re: little gee and its sign



Regarding Jim Green's peeve:

But I think that the greater difficulty in this case is the reference
to g,
a gravitational variable, as acceleration. It is not. The force mg
may
perhaps lead to acceleration -- or it may not -- but "g" is not
acceleration in any case.

Jim's point is well taken, but he is too adamant here by saying 'in any
case'. The fact is g_vec *is* an acceleration. It is the local
acceleration of a freely falling locally inertial frame in which its
value vanishes w.r.t. the coordinate system in which it has its
particular value for the observer's frame. Also, -g_vec is an
acceleration, too, being the local acceleration of the observer's
coordinate system in which g_vec appears with its particular value as
the gravitational field w.r.t. a freely falling locally inertial frame
in which it vanishs.

BTW, it is not clear to me just exactly when the best time is to spring
this revelation on the students. I suspect that doing so too early in
their physics student career would be counterproductive. But it would
be good for them to realize and assimilate this fact before, and without
having to take, a formal GR course where they would then have to deal
with it in a more intimate way. It goes a long way in explaining why
the gravitational force on an object is always proportional to its mass,
as well as explaining Galileo's inference of the universal acceleration
of freely falling bodies being independent of their composition and
mass. Besides, the vast majority of intro students will never have the
luxury of the latter course. Often the Equivalence Principle is
introduced in a 2nd year modern physics course. Is this best, or should
we include it at the intro level? I confess to trying to do the latter
(at the end of the relativity unit which had earlier dealt almost
exclusively with SR) and hoping for the best.

David Bowman
David_Bowman@georgetowncollege.edu