Spin is angular momentum

If you've taken an introductory chemistry course, chances are good that you've heard of a property of particles called spin angular momentum, or spin for short. In chemistry, spin is particularly relevant to the way that electrons can pile into atomic orbitals. More generally, in quantum physics (or particle physics), all fundamental particles have spins, and spin plays a huge role in the interactions between particles.
In any case, the spin statistics theorem (which basically describes the difference between leptons, which are the standard particles you hear about (electrons, quarks, etc.), and bosons, which carry forces) is a topic for another day. Instead, I want to briefly mention a really cool property of spin. I've heard it called 'spin angular momentum' for a long time, and it has some distinct parallels with orbital angular momentum. It's also almost always described as a tiny little particle rotating around its axis. But until recently, I didn't realize how very angular-momentum-ey spin actually is. There's this effect called the Einstein-de Haas effect that shows very clearly how spin is part of the total angular momentum of an object.
Imagine that we have a long(ish) thin cylinder of a ferromagnetic material like iron suspended from a twistable wire or thread. Wrap a conducting wire around this cylinder many times to create a solenoid (but don't let the solenoid touch the cylinder - that would a) short out the circuit and b) make it hard for the iron to rotate). Now run a current through the solenoid, which creates a roughly uniform magnetic field inside the cylinder, pointed along the cylinder. Because the cylinder is a ferromagnet, this polarizes the spins of the electrons inside along the magnetic field. All this is old news. The fascinating thing, and the fact that makes it clear that spin really is angular momentum, is that in order to conserve angular momentum now that all the spins are pointed in the same direction, the ferromagnetic cylinder starts to rotate in the opposite direction. This is the Einstein-de Haas effect, and it was theorized and observed by (surprise surprise) Einstein and de Haas in the early 20th century.
The reverse is also true, in what's called the Barnett Effect. That is, if you rotate a ferromagnetic material, it can spontaneously develop a magnetic polarization! So the angular momentum of the object is partially cancelled out by an alignment of the spins, which produces a net magnetization in the material.
Physics is awesome.