The result that Noether obtained was stunning. She showed that to every continuous symmetry of the laws of physics there corresponds a conservation law and vice versa. In particular, the familiar symmetry of the laws under translations corresponds to conservation of momentum, the symmetry with respect to the passing of time {the fact that the laws do not change with time} gives us conservation of energy, and the symmetry under rotations produces conservation of angular momentum. Angular momentum is a quantity characterizing the amount of rotation an object or a system possesses {for a pointlike object it is the product of the distance from the axis of rotation and the momentum}. A common manifestation of conservation of angular momentum can be seen in figure skating-when the ice skater pulls her hands inward she spins much faster.
( Mario Livio )
[ The Equation That Couldn't Be ]
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