Re: ACCELERATION

[Leigh Palmer <palmer@SFU.CA>]

At 5:59 AM -0700 9/15/00, Michael N. Monce wrote:

> On Thu, 14 Sep 2000, Leigh Palmer wrote:
>
> > What has been implicit here is that one is talking about the motion of a
> > massive extended object - and idealizing it by discussing the motion
> > of a point having no size - or substantial reality!
>        True, we generally talk about such motions with regard to points,
> but don't we also show that the motion of an extended object, or group of
> smaller objects, can be described by applying Newton to the
> center-of-mass; a point of no size.  So motion of extended (real) objects
> can be modeled quite accurately by using a single point.

That is just the <point> I made in my earlier sentence:

> > These kinematic quantities
> > pertain to the motion of something abstract, usually a point in space
> > defined by a formal procedure defining the center of mass of some
> > physical object.

While the description is quite accurate (in fact it is exact, since the
motion of the center of mass of the object is mathematically defined),
the description of the motion of an extended object is not *complete*.
This model is complete for a rigid body, but there are no rigid bodies.
The rigid body is an abstraction.

In particular, when one asks questions about discontinuous acceleration
one must consider how the model differs from reality on the shortest of
timescales. Now hysteresis rears its ugly head. The velocity of a rigid
body depends upon the velocities of all its constituent particles, and
on the shortest timescales these velocities are not all the same even
in the case of nonrotating bodies. The presence of sound waves within
the body will serve as one of a number of examples.

I think that it is important for us to recognize (and share with our
students) the fact that we are teaching models having limited validity.
When a question like "Can a real body have discontinuous acceleration?"
arises, the only honest answer must recognize the limits of validity of
the model. Since, above all, we must strive to be honest in teaching,
these niggling points about validity should be introduced, even though
you may feel they get in the way of understanding.

When I was in grad school I took a quantum solid state course from
Charles Kittel. Despite a severe stutter, Kittel is an execellent
teacher. One lecture he gave in the course, however, left me cold and
annoyed. Kittel derived the model which demonstrates some effect of
parallel pumping in solids. After a smooth derivation with no evident
problems, at the end of the hour he said something like "I suppose I
should tell you that I've swindled you a little bit here. If I had
pumped with sine omega t here instead of cosine omega t, the whole
effect would go away." He left it like that.

I learned no physics from that lecture; it was a waste of my time.
The very least he should have done was to warn us at the time he
swindled us (when "the frog jumped into the pond") that he was doing
so, and he should have made a slightly longer statement at the end
explaining why this derivation still had merit.

Rigor in the pursuit of learning is no vice.

Leigh