Re: The Olympics

[Mark Sylvester <msylvest@XNET.IT>]

At 15:50 25/09/00 , Michael Edmiston wrote:
> I am not sure I believe what Mark Sylvester is saying.  He seems to be
> saying that a translating object can convert some of the translational
> kinetic energy into rotational kinetic energy, and I don't see how that is
> possible unless the object has contact with another body or bodies.

Not translational k.e.
Energy from the muscles is used. But it's angular momentum that you have to
worry about: it has to remain zero in the absence of an applied torque.
This is achieved by the cat by twisting so that the front part of the body
has L and the rear part -L, but with different omega values because the L's
are different. Thus in the same delta t, the rear end twists clockwise
through a bigger angle than the front end twists anticlockwise (eg). Then
by sticking the rear legs out and pulling the front legs in, and reversing
the twist, the rear comes back through a smaller angle and the front
through a bigger angle, and a net change of orientation is achieved,
angular momentum staying zero throughout.

> Of course there is air friction.  I think we will readily admit that air
> friction can be utilized in the case of a sky diver.  For Olympic divers the
> speed is too slow and the time to use air friction is too short.  For cats,
> maybe they have more friction, and maybe more time (depending upon the
> height of the fall) but I doubt the typical falling cat has sufficient time
> to make use of air friction like sky divers do.

Exactly. Drop a cat upside-down from about 2 metres and you'll see the
quick thrusting movements of the legs as it does what I've described. I
imagine that we'd learn to do something similar if we spent enough time in
free fall and had to change orientation without touching anything.

> I agree that the angular position of an animate object can be changed by
> judicious rotations and counter-rotations combined with center of mass
> shifts.  But these manipulations only change the orientation, not the
> angular momentum.  For the falling cat, this might be the goal.  For the
> Olympic diver I think it is slightly different....

deletions

> ...initial angular momentum, these extreme cases would present very different
> problems to the cat.  I think Doug Craigen was also trying to tell us this.

All of this is perfectly clear, but Doug's comment I replied to suggested
simply that in free fall one can achieve *neither* a net displacement nor
rotation in the absence of an external push. I'm pointing out that while
this is true for translational motion, it's not true for rotational motion.
You *can* achieve a net rotation while maintaining zero angular momentum,
the difference being that you can play around with I but not m.

Any other good pheline physics that we can discuss?

Mark.



Mark Sylvester
United World College of the Adriatic
Duino TS Italy
+39 040 3739 255