Re: ROTATION

[John Denker <jsd@MONMOUTH.COM>]

At 07:09 AM 9/7/00 -0400, David Abineri wrote:

> If a long thin rod is rotating about one end is it also rotating about
> its center?

Yes.

1) The question is tantamount to asking for the definition of
"rotation".  The operational definition is robust and
straightforward:  Imagine there are observers attached to the rod.  Each
observer has a set of gyroscopes.  The gyroscope axes are a local
definition of constant orientation.  All observers report that the rod is
changing its orientation at a rate Omega.

(Nitpickers note we are neglecting General Relativistic effects here;  i.e.
we assume all velocities are small compared to c.)

2) Note that there are other ways of detecting rotation.  These include
observing the centrifugal force, which is sensitive to
  Omega cross Omega cross r
in contrast to the gyroscope which is directly sensitive to Omega.

> If so, what is the relationship between its angular
> velocity about its end and its rotational velocity about its center?

Equality.

A familiar example of this is the moon, which orbits once a month and spins
on its axis once a month.