Eli5: Angular momentum, how does it work?
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There are good explanations of how angular (and linear) momentum “works” in the sense of how to describe its effects, but they don’t really address *why* there is angular momentum. What causes these effects we can describe.
The answer, weirdly enough, is that angular momentum exists because physics looks the same no matter which direction you face. Linear momentum exists because physics looks the same no matter where you are.
In 1915, Emmy Noether proved that if a physical system has a smooth symmetry, then it has a corresponding conserved quantity. For instance, if you set up an experiment in a train car on a straight track the results will be the same no matter where along the track you park the car. Similarly, if your lab can rotate the results of the experiment don’t care what direction you face. If there weren’t something like angular momentum that we can measure and never changes for a closed system, then you could set up an experiment that could tell what direction you were facing. If there weren’t something like linear momentum, you could set up an experiment entirely within your train car that could tell where along the track you were.
There’s one more conservation law you probably know: conservation of mass-energy. This corresponds to the fact that the laws of physics stay the same through time. All conservation laws correspond to symmetries like this. Thanks, Emmy!
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