I read the information at the web site referenced by Bruce Esser. I only
read through it once, but I think it is correct and it made sense to me.
I think (and others have implied the same) that what gymnasts say, and what
we think they say, might be different things. What does it mean if a
gymnast says she must not impart angular momentum (twist) upon leaving the
horse (or whatever prop is being used)? What does she mean when she says
she must launch herself "straight?" Certainly gymnasts are imparting an
angular momentum vector that runs from their right to their left because
they initiate a forward tumble as they bend over to place their hands on the
horse and then somersault over.
Thus, when they say they cannot "twist" they must mean about some other
axis, presumably they must not twist around any axis in the plane that
contains their forward motion.
I can buy that... gymnastic judges can define vaulting etiquette any way
they want, and if said twists are improper, then so be it. But there is
clearly an angular momentum vector running right to left during the vault if
the hands are placed on the horse and the feet go over the top.
While David Bowman's statement about conservation of angular momentum may be
true, I think the implication some people draw from it is false. I think
some people might think he means that an object cannot be spinning about one
axis and then end up with some spin about another axis unless there is an
external torque. This implication is clearly false.
An example that is useful, though not exactly the same as moment-of-inertia
changes, is the common demo of standing on a platform that can rotate while
holding a spinning bicycle wheel. Suppose the beginning condition is
similar to the gymnast with the angular momentum of the bicycle wheel
pointing from right to left as the wheel is held in front of you, and there
is initially zero rotation of your body as you stand on the platform. Now
twist the bicycle wheel so its angular momentum vector points up. Your body
will begin to turn as the internal torques (treating you and the wheel as
the system) adjust to conserve angular momentum.
This is what the web page (that Bruce referenced) says to us... that moment
of inertia changes that are asymmetric with respect to the original angular
momentum vector can impart new rotations (i.e. about a new axis). This is
not a violation of conservation of momentum (like some people might infer
from what David Bowman said). Rather, the "new rotations" about a "new
axis" indeed are required to conserve angular momentum when the moment of
inertia changes in an asymmetric way.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817