Here is a cool example of a case where it ostensibly seems like angular momentum is not conserved but the resolution is quite cool, and quite alien if you are new to thinking of classical fields as "physical" entities.
Imagine we have an infinitely long solenoid of radius ##R##, current ##I##, and turns per length ##n##. Furthermore, imagine we have two coaxial cylindrical shells of length ##l## with one at a radius ##a < R## from the common axis and one at a radius ##b > R## from the common axis (so one is inside the solenoid and one is outside). Let the inner shell have a charge ##Q## and the out shell have a charge ##-Q##, both uniformly distributed over the surfaces. Now if you start reducing the current in the solenoid to zero, you will start to see the cylinders rotate (you can show this mathematically as well but I won't go into that)! So it seems like they starting rotating out of nowhere. But we know for a closed system that the angular momentum must be conserved so where is the angular momentum coming from that is resulting in the rotation of the cylinders?
Well it turns out that the angular momentum that the cylinders acquire when the current reaches zero actually comes from the angular momentum of the initial electromagnetic field itself! If you are familiar with the theory, this would be a fun little example for you to work out by yourself and verify that the angular momentum of the initial EM field is exactly equal to the angular momentum of the cylinders once the current goes to zero. This is more or less the same as Feynman's so called disk paradox.
On a related, but even cooler note, look up what is called Thomson's dipole.