So I was just reading a bit about magnetic dipole moments, Larmor precession, angular momentum etc., but there was one little thing that was bothering me. As far as I know, any angular momentum will precess around any magnetic field, no matter how big the angular momentum and the magnetic field is. So the angular momentum can be as small as you like. So then I thought about bar magnets, which I thought had a very tiny amount of angular momentum due to their magnetic dipole moments, for as we know, the magnetic dipole moment is the gyromagnetic ratio (gr) times the angular momentum. But of course, the gr is really big for bar magnets because it's so large for electrons (and as we know, it is the electrons that make up the currents that are creating the magnetic field of the magnet). Thus, the angular momentum of bar magnets must be microscopically small. But again, as I said, any angular momentum will do, meaning that bar magnets should actually precess. What is wrong with my thinking here?
If the object precesses or not, or does something inbetween, namely nutate, depends on the ratio of Larmor frequency to the rotation frequency of the object. If you start from a situation where the magnet is tilted with respect to the field and then you let go, you obtain perfect precession only, if the rotation frequency is infinite. One may think of electrons, which are point-like with zero moment of inertia, as having infinite rotation frequency for their finite angular momentum of hbar/2. For any object with a spatial extent and non-zero moment of inertia, the transition from perfect precession to "swinging" is gradual, depending on the size of angular momentum and thus rotational frequency.