Re: The Olympics

[Maurice Barnhill <mvb@UDEL.EDU>]

I agree with your girlfriend that none of the twisting, etc., discussion
explains what happens in diving and gymnastics.  I believe that the
crucial point is off-diagonal moments of inertia, so that the asymmetry
of the position taken to start the twisting movement is crucial.

Angular momentum is conserved, but angular velocity is not.  If  L  is
the angular momentum and  w  is the angular velocity, the full
expression for  L  is

L/i\ = sum I/i j\ w/j\

The moment of inertial tensor  I  can have off diagonal terms, so that
the angular velocity is not parallel to the angular momentum.  Hence if
you change  I  , for instance by moving your arms and legs around or by
bending at the waist, you can change the direction of angular velocity
without changing the direction of angular momentum.  Hence you can
convert a tumbling rotation to a twisting one without applying a torque.

I forget where I first read this explanation, and I don't know how to
implement it in detail since the actual motion is complicated. However,
I am sure that this is the qualitative physics involved.  Nothing else
fits the descriptions of the athletes themselves.

Zach Wolff wrote:
> There seems to be general agreement from list members
> that divers and gymnasts either leave the ground or
> board with some angular momentum or perform
> complicated gyrations, moving one half the body then
> the other, to execute a mid-air twist.  My girlfriend,
> a gymnast, argues that this is not so.  She claims
> that it is important to leave the ground with no
> rotation whatsoever and that move required to twist is
> simply to draw both fists to the one shoulder and turn
> the head toward that same shoulder, causing a rotation
> in that direction.  I am unable to understand how this
> could possibly cause the rotation in the intended
> direction.  It is possible that her intuitions are
> incorrect.  Only stroboscopic pictures would reveal
> the truth.  However, her argument is strengthened by
> two factors: one, she claims that leaving the ground
> with any rotation leads to a point deduction and
> judges are watching very carefully, two, she claims
> that it is possible to decide which way to twist AFTER
> leaving the ground.  She makes the same claims for
> diving where she has some experience, but not at a
> competitive level.  Can anyone make sense of this
> data?
>
> Zach
>
> > On 24 September 2000 Justin Parke wrote:
> > > Perhaps the answer to this question should be
> > obvious to me, but after
> > > pondering for a while have not been able to answer
> > it.
> > > It seems that the divers in the olympics (and the
> > "trampoliners") are able to
> > > execute  half-twists, beginning and ending the
> > twist in mid-air.  I do not
> > > know how they do this without violating
> > conservation of angular momentum.
> > > Could someone enlighten me?
>
> __________________________________________________
> Do You Yahoo!?
> Send instant messages & get email alerts with Yahoo! Messenger.
> http://im.yahoo.com/

--
Maurice Barnhill (mvb@udel.edu)
Department of Physics and Astronomy
University of Delaware
Newark, DE 19716