Eli5: Angular momentum, how does it work?
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All momentum is an offshoot of inertia, which is an object’s tendency to keep doing what it’s doing, whether that’s being still or moving. Angular momentum just refers to spinning instead of linear movement.
Think of a spinning top; even though you only held it and accelerated it for a bit, it still keeps spinning for a while after you’ve let it go. Of course, friction and drag eventually slow and stop it.
The other aspect of angular momentum is where the mass is located on the object. For linear movement/momentum, the entire object is moving at the same linear speed; one part of a falling apple can’t be moving faster than another. For a spinning object, however, that’s not true.
A point near the center of the object (or the axis of rotation) is moving slower than a point at the edge; this should be evident by the formula for an object’s circumference, where the circumference of a circle (which is the distance covered in one rotation) is dependent on the diameter of the circle. Larger diameter, larger circumference, longer distance over the same time (one rotation), faster movement.
So when you are spinning on an office chair with your legs out, there is a lot of mass that is far from the center of the chair, moving fast. When you bring your legs in, the mass moves closer to the center of the chair and moves more slowly. This changes the momentum of the spin, which can’t happen unless you put energy into the system to accelerate/decelerate it. The only solution is that the speed of rotation goes *up* so that the momentum (mass/*speed) is still the same.
It’s a lot like regular momentum but for rotating objects, linear momentum gives you a measure for how hard it would be to stop something from moving. Similarly angular momentum gives you a measure for how hard it would be to stop a rotating object from moving.
But because in rotating object not only the mass matters but also how far away that mass is from the centre of rotation the angular momentum uses the moment of inertia instead of simply the mass of the object.
Angular momentum also uses angular velocity instead of the regular velocity.
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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