Angular Momentum of Point Particles

[Darkmisc]

Does it make sense to think of a point particle's rotation? Or does the particle need to be more than one point in dimension so that parts of it can exist either side of an axis of rotation?

 

[LukeD]

If we have a universe with nothing but a point particle, and we rotate our universe, nothing changes, so we can't talk about the angular velocity of a point particle, and if it's rotating, we can't sensibly talk about how much of an angle its rotated by.

However, let's say we have 2 particles attracting each other by gravity so that they rotate with some angular momentum L. If we allow the 2 particles to collapse to a single point, because angular momentum is conserved, the single point still has angular momentum = L. (But the angular velocity goes to infinity! A point particle with angular momentum seems to spin infinitely fast)
If the single point would then split into multiple particles, the group would still have angular momentum = L, and we could again sensibly talk about angles & angular velocities.

So no, we can't talk about the speed or angle of rotation of a single point particle, but we can talk about its angular momentum.

It may not surprise you to hear that electrons are point particles that always have $$\hbar/2$$ of angular momentum about some axis.