Answer to the Question 09/04

FRICTIONLESS ROTATION

The question was:

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?

(5/05) Y. Kantor: We received a very large amount of proposed solutions. (We will not list the names of the numerous contributors, but we wish to thank them all.) Roughly, the solutions fall into three groups:
a. Using external objects. E.g.: Take off your shoe and rotate it above your head.
b. Actively use the ice as a provider of normal force. E.g.: Lie down on the ice, and, by pushing with hands turn around on your back; then get up.
c. Use body motions to perform the rotation. (The fact that the ice supports you is used to the "minimal extent.")

The solution presented below does not follow exactly any of the proposed solutions. Nevertheless, it follows the "spirit" of some of the proposals mentioned in the item (c) above.


The solution: Since it is a bit difficult to explain the nature of the moves, I hope that the demonstration by my son in the pictures below, will help you to visualize the required motion.

The rotation is accomplished by repeated sequence of hand motions as described below:
Bend your hand and the stretch it out forward.
Swing it sideways and as a result your body will rotate in the opposite direction.
Bend your hand back.

The idea of the entire exercise is that when you swing your hand, the moment of inertia of the entire body is different from the moment when you bring the hand back to the original position. Such change in the moment of inertia is a necessary condition for performing this rotation.

Comment: It should be noted that the act of stretching the hand forward on a frictionless ice is not a trivial accomplishment. The fact that one does not fall down (due to rotation of the body in the opposite direction), is due to the small momentum of force that can be generated by the normal forces of ice acting on our feet.
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