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.
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.
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. Yes, the diver is trying to
change the angular position, but I think control of the existing angular
momentum (created upon leaving diving board) is the primary feat being
accomplished.
Thus, although similar, I think the cat (assuming it was dropped with zero
angular momentum) and the Olympic diver (who gives herself an initial
angular momentum during "launch") are slightly different. That is,
"controlling the angular velocity" and "changing the angular position" are a
bit different.
I think John Clement made the important statement when he pointed out that
the diver gives himself a certain amount of angular momentum when he leaves
the diving board. This leaves a couple "tricks" the diver has to master...
(1) what is the right amount of angular momentum to give (because too much
or not enough and he won't be able to compensate)... (2) what body
"gyrations" are necessary to control the angular velocity in order to
accomplish the dazzling effect desired, yet enter the water with the desired
angular position.
Therefore, the primary way this differs from the cat is the cat does not
launch itself with a definite angular momentum that it then utilizes. That
does not mean cats would be unable to use whatever angular momentum they
happen to have... perhaps they can figure that out quickly. But I presume
if cats were given a high amount of initial angular momentum versus zero
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.
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