A non-trivial result from studying the classical mechanics of an extended object shows that rotation about an axis whose moment of inertia is between the largest and smallest moment-of-inertia axes is unstable. This is known as the "tennis racket" theorem, as described on the Wikipedia page. In essence, there are two axes which are easy/stable to rotate around, and one which is unstable.
The basic idea of the tennis racket theorem has little to do with gravity or air resistance, but it a statement about the sensitivity of the resulting rotation axis to the axis of the initial torque. Very nice videos demonstrating this concept can be found on YouTube. For example this one.
My question is the following: is there a quantum analog of the tennis racket effect?. If there is, I suppose this theorem would have some relevance to the physics of molecules and their rotational properties, perhaps even their interaction with light in say optical tweezers. I'm also guessing that the theorem might hold at high temperature/energy where things are kind of classical but should break down at low temperature/energy.