Ok so you want the flaw in your reasoning. Imagine a hula hoop. It’s spinning, but otherwise not moving. Mentally divide it up into lots of little chunks. Eac

Ok so you want the flaw in your reasoning. Imagine a hula hoop. It’s spinning, but otherwise not moving. Mentally divide it up into lots of little chunks. Each chunk has a little bit of linear momentum. 1. Is each chunk’s linear momentum constant in time? No, because its direction of motion is changing. Hm, that’s unfortunate. 2. What about if you do R x p, the radius of the loop crossed with the momentum of that little chunk. That gives you a quantity for each chunk that’s unchanging. That’s called the angular momentum of that chunk. If you add the angular momentum for all the chunks, you get the total angular momentum. So you see that angular momentum works just like linear momentum. You take a conserved quantity for a single chunk and add up over all the chunks. You’re free to think of all the little particles and their linear momentum, but that isn’t so useful, since summing the linear momenta gives you zero, whereas summing R x p gives you something to reason about.