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Application of angularmometum

Angular momentum is conserved, and that is why (figure1)skaters can perform dazzlingly fast spins. First, with arms and leg stretched out, the figure-skater's rotation is slow:

 

Figure1-skater with arms and leg stretched out

His whole body is turning on a vertical axis. All the different parts of it - except for the tiny portion directly where the axis intersects the body - have non-zero angular momentum. For each portion of the body, this angular momentum is given by the mass times the distance from the central axis times the orbital speed.

If the figure-skater now brings his arms and legs in line with the rest of his body, as in the (figure2)below, the distance of those body parts to the axis of rotation decreases significantly. Yet the total angular momentum must remain the same (the amount of angular momentum the figure-skater imparts on his surroundings, for instance on the air around him, is negligible). If, in a product of several factors, one factor becomes smaller, yet the product is to remain the same, at least one of the remaining factors must grow larger. For our figure-skater, the compensating factor is the speed of his rotation, which increases markedly. The result is a very fast spin.


 


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