# Is it possible to rotate an angle on perfectly smooth ice?

You must start and end with the same pose.

Prove it if you think you can't.

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Do you mean that I'm standing on the ice and pushed to only rotate around by backbone for 360 degreed exactly? Yes it is possible, but theoretically it can happen when you balance two forces (ie. right shoulder is pushed forward, left backward) that will gain you the exact amount of energy needed to rotate you that way. – Crowley Jun 3 '11 at 6:45
No, it won't, you will temporarily rotate a little and stay still with your shoulders pushed, but you will immediately back to your orientation when you get back to your original pose. – trVoldemort Jun 3 '11 at 6:51
It seems You used a laymans expression: "perfectly smooth ice", when meaning a friction-free surface. Ice can be as perfectly smooth as You want, the friction will be small, but never zero. Because surfaces without friction do not exist in real world, You have to name this condition expressis verbis. – Georg Jun 3 '11 at 8:31
I supposed non-deformable shoulders, so those two forces are converted in momentum without any loss, and being pushed by someone else. If you mean rotating yourself on real smooth ice you should remember that static friction is higher than kinetic one, so your impulse given by twisting your arms CCW will be thansformed into rotatin more effective than returning back CW. – Crowley Jun 3 '11 at 8:54
All you gotta do is swing part of yourself, like a leg or an arm, in a circle. (Satellites do this by means of reaction wheels.) – Mike Dunlavey Oct 25 '11 at 12:21

Yes, it is possible. This is an example of the cat-righting problem.

You simply must change your moment of inertia during the process.

Model your body as two cylinders of equal mass which can exert forces between each other to start spinning. The bottom cylinder has an adjustable radius, initially set equal to the top cylinder's.

Set the top cylinder spinning CW. To conserve angular momentum, the bottom cylinder spins CCW at the same angular frequency.

Wait a short time, then suddenly increase the radius of the bottom cylinder and simultaneously make the top cylinder change directions to start spinning CCW at the same angular frequency as before. The bottom cylinder will start spinning CW, but since its radius is increased, its moment of inertia is higher, and its angular frequency will be smaller than before.

When the two cylinders are lined up relative to each other, stop them both, and return the bottom cylinder to its original radius. The entire apparatus must have rotated because the top cylinder's angular frequency had only a one absolute value the entire time, but the bottom cylinder had two. They therefore had different total angular displacements, so the entire thing must have rotated.

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Mhhmmm, the movies I have seen showing falling cats, were thus that the cat started to rotate the tail and kept rotating it until the cat landed on its feet. BTW Your link: I always thought that cats are very intelligent, but that they know about Yang-Mills theory, that is really astonishing! :=) – Georg Jun 3 '11 at 8:37
I asked a cat to explain Yang-Mills theory to me once but it didn't answer. I think she thought it was so obvious that it was beneath her to have to spell everything out for me. – Mark Eichenlaub Jun 3 '11 at 9:29
I once had a cat who did not stoop to answer questions on GR. :=( – Georg Jun 3 '11 at 10:40
That sounds a bit complicated. Simply make your arm rotate above your head, i.e. you can move your hand in a circle above your head. Because of conservation of angular momentum, the rest of your body counterrotates. Stop when you have rotated the requiste amount stop. – Omega Centauri Jun 3 '11 at 14:11
@omega good point - I didn't think of that. Thanks. – Mark Eichenlaub Jun 3 '11 at 14:58