Re: The sign of g

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 16:55 -0600 9/4/02, Larry Smith wrote:
> Ahhh, it is more than a mere choice of words; what do we really _mean_ by
> g?  And they don't have the same value; i.e. the acceleration of objects in
> free-fall near the surface of the earth is not the same as the local
> gravitational field vector.  The former is affected by the spinning earth,
> the latter (in classical physics) is not.  The values of g in x = (1/2) g
> t^2 and F (or W) = mg are not technically the same if the latter g is the
> field strength.  And while the dimensions are the same, the units usually
> reflect whether we are meaning an acceleration (m/s^2) or a field strength
> (N/kg).
All this is correct, but should we burden beginning students with
what are at best second-order corrections that will only impede their
progress? There is a problem in H&R that addresses the issue of g's
direction being skewed away from the true vertical by the effects of
the earth's spin, and my second-year students had a great deal of
trouble with it. These were top students, several of which have gone
on to earn PhDs in physics and related fields. There is time enough
to mention that the local value of g has some corrections that make
it differ from the true gravitational field when we start to talk
about circular motion. And with a first-year course, I would do no
more than mention it in passing, perhaps pointing out that this is a
subject for a more advanced-level course.

If we cross every t and dot every i at the beginning of the students'
study of physics, they will be so overwhelmed with details that we
will get in the way of their basic understanding. One thing we do is
to point out at every opportunity that there are complexities to the
subject, but that they either will be dealt with later or are
appropriate for a later course. It is important for the students to
understand that there is a reason for introducing them to the ideas,
and no idea should be introduced before it is needed, as Arons has
pointed out, but one has to start somewhere.

I believe that it is also important to give a new idea a bit of
gestation time before we dive into it, so I have introduced some
ideas (like, for instance, relative motion and center of mass) early
on, because they are new and need getting used to, a bit before we
actually use them (when we get to momentum). At that point a quick
review of the idea is usually enough to get them on track and using
it correctly.

This approach may not be everybody's cup of tea, but it seems to work for us.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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