A craze of 'fidget spinner' toys has broke out recently in my hometown. If you are unfamiliar, they are basically just discs with a fixed joint and ball bearing at the center so you can rotate them while you hold the center (because of the design, there is clear fixed axis on which you are supposed to rotate it, so I will refer to this as the axis of rotation throughout the post, despite talking about rotating on separate orthogonal axes as well)
I noticed that if the disc is still, you can throw it up and flip it off of its axis of rotation with ease. It will continue to spin until it is stopped (either by catching it or hitting the ground). However, when it is spinning, you are not able to do so. It may turn slightly, but it rapidly reaches an equilibrium where it will continue to to rotate only on its natural axis of rotation.
My question is why this happens. I'm sure it has something to do with angular momentum, or perhaps torque, but I am unsure how to expand upon or prove my intuitions (I am a mathematician, myself, and proving physics concepts has always been an irritant of mine).
Ideas began to run through my mind, such as the relation of this concept to disc shaped (spiral) galaxies and solar systems. Of course, this likely differs in that the bearing cause the toy to spin much smoother on a particular axis, where it seems to me the cosmological examples above have an arbitrary axis of rotation (as in the Physics does not change if the axis had been different)
Of course, if I'm not explaining the situation well enough, let me know in the comments and I'll try to give more detail