Discussion of the Question 09/04
FRICTIONLESS ROTATION
A man is standing straight on the surface of ice facing east.
The ice is so slippery
that there is no friction between the man's shoes and the ice. Is there
a sequence of moves that can be made, such that at the end of it the man
will be standing straight facing west?
(11/04) Y. Kantor:
We recieved a surprisingly large amount of e-mails containing the statement
that angular momentum conservation implies a "direction conservation."
This prejudice is extremely common among physicist, and is particularly
visible in answers that they give to a question "How does a cat fall
on its feet." In various web-sites you can find answers ranging from
"the cat is rotating its tail at high speed" to "the cat
always(!) has an initial
rotational velocity which it then regulates by spreading its feet
like a rotating ice-skater does with his/her hands". In fact a body
which can be deformed in its shape does not have to preserve its
orientation.
T.R. Kane and M.P. Scher, in Int. J. Solids Struct. 5, 663 (1969)
"mapped" the motions of a cat on two cylinders which can rotate and
change the angles between their axes. They showed by detailed analysis of
equations of mechanics, how a cat performs the "impossible rotation."
[See more in R. Montgomery, Fields Inst. Comm. 1, 193 (1993)
and J. Marsden, in Motion, Control and Geometry (Nat. Acad. Press,
Washington, D.C., 1997).]
In fact, already in 1894 Etienne-Jules Marey and
Georges Demeny made a movie that shows in great detail the way
a cat thrown upside-down (without any initial rotation) turns
over during a short fall.
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