Re: ROTATION

[John Denker <jsd@MONMOUTH.COM>]

At 09:47 AM 9/7/00 -0400, Robert A Cohen wrote:
> students have difficulty seeing the rotation as a rotation about an axis
> other than the axis going through the earth's poles

An excellent insight.

At 07:11 AM 9/8/00 -0700, John Mallinckrodt wrote:
> 1) Unfounded expectation that the center of mass, a pivot point, or
> a fixed axis should, somehow, be afforded special consideration

Good point -- a more general formulation of RAC's point.

> 2) Unfounded expectation of interactions between the translational motion
> of an arbitrary point and the angular velocity

Another good point.

To illustrate the distinction, consider the following examples:
 -- a vortex in a low-viscosity fluid, which is (to an excellent
approximation) irrotational (outside the core), but which has lots of motion.
 -- a nonspinning object in orbit, e.g. the space telescope maintaining a
view of a given distant star.  Lots of translational motion, no spin.
 -- contrast that with the moon, which orbits once a month and spins once
a month.

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At 07:11 AM 9/8/00 -0700, John Mallinckrodt wrote:
> the author refers misleadingly IMO to the angular
> velocity "of" arbitrary points attached to a rigid body (rather
> than the angular velocity of arbitrary points attached to a rigid
> body relative to other arbitrary points also attached to the rigid
> body)

I wouldn't have said that, for several reasons.

1) Rotation is not relative.  An angle (angular position) is relative, but
if the object is rotating, the rate of rotation (angular velocity) is
absolute, not relative.  If you insist on measuring "relative" to
something, it should be "relative" to local gyroscope axes or the
equivalent.  It is an important principle of physics that all local
gyroscopes agree that their axes are all nonrotating.

You certainly can't measure rotation relative to other points on the same
rigid object.  By definition of rigidity, the whole object rotates the same
way.

2) This is a subtle point for aficionados;  others may ignore it:  I'm
skeptical that it is possible to define rotation of a _point_, strictly
speaking.  I can visualize rotation of an object (or a piece of fluid) in
the _neighborhood_ of a point.  That is, I can imagine a triad of axes with
infinitesimal (not zero) size attached to a point.  I can imagine
gyroscopes with very small (not zero) size.  But rotation of a genuine,
zero-sized point is highly problematic.

If anybody speaks of rotation "of" a point I will assume he meant "at" that
point which is shorthand for "of the stuff in the neighborhood of" that point.