Re: The Olympics

[Doug Craigen <dcc@ESCAPE.CA>]

Ludwik Kowalski wrote:
> This makes me think about a cat released in the
> legs-up position. Cats always land on their feet.

Not always.  Perhaps I shouldn't admit this, but as children my brother
and I were curious about this and performed some careful experiments
over our beds and at heights of no more than a foot (no cats were hurt,
only their egos).  When you release cats they usually manage to generate
some amount of twisting.  First of all, its hard to release them with
zero angular momentum and they will do all in their power to generate
some sort of kick off to set themselves spinning.  They will also twist
the ends of their body in opposite ways.  For example, as you hold its
feet up it twists its head around to look at the ground. When released
its head spins one way while its body spins the other.  Even though the
body has much more moment of intertia, this is part of the "trick".  In
fact, they don't land on all fours simultaneously. By twisting the body
they can get two feet to land, and then using the ground for leverage
twist the rest of the body for the other feet to land.  But, until
hitting the ground there was no net rotation.

These "experiments" go back 30 years, so my recollections are vague.
However, if you release a cat very carefully from feet up and facing up
it has a hard time landing on its feet.  Further, if it can't see
clearly how high it is then it will likely over rotate - so it is unable
to magically stop a spin.  As commented below for divers, I suspect that
in longer falls they can use air resistance to their advantage.

(Incidently, does anybody have solid references on the survival rate of
falling cats increasing after something like 10 stories?  That's one
experiment I don't plan to do.  Supposedly this is about where they
reach terminal velocity so that it shouldn't matter how high they fall
after that, but various things come in to their advantage such as being
well positioned - possibly in a position with a slower terminal
veloccity - and more relaxed for the impact.)

> Ludwik Kowalski
>
> 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?

I haven't watched the trampoliners, but the divers seem to me to do it
much like figure skaters.  Start with a high torque kick in a straight
(high moment of intertia) position.  Tuck in to lower your moment of
inertia which speeds up the spin rate to conserve angular momentum, then
straighten out to raise the moment of inertia and slow the spin down
again.  In the slow motion replays they are clearly still spinning as
they hit the water, just more slowly.  As their vertical speed has
picked up by then one gets even more illusion of going straight down.
Also, I wonder if air resistance provides some benefit to divers as they
get to higher speeds at the end.

\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\

Doug Craigen
          http://www.dctech.com/physics/about_dc.html