Hey, Klaas. I think I understand your coin situation. I think the reason is sort of a combination of all these things. I think if the coin is thrown slightly tilted, then when its centroid is further to the side than the contact patch, it would begin to fall to the side. Since it is rolling, the falling begins a precession that counters the fall and begins making a circle. But, I couldn't make a coin do the behaviour you described so I may be misunderstanding, or uncordinated, or both. I see why this massless situation messes with your intuition. I thought a while about it and came up with this: As you look down on a rider on a unicycle, the polar moment of inertia is small (the inertia resisting rotation about what we have been calling the y axis)(we weigh a lot (some more than others), but our mass is all pretty much very close to the axis). The angular momentum of a turning wheel is probably pretty significant (spin a wheel and try to tilt it without letting it precess, it will fight with you pretty hard, even for light wheels) these two things sort of work together to make a pretty significant effect.
I am not for sure yet, but looking at the equation it seems that a decrease in the mass of the wheel means that there is a smaller required force to make the same precession. As I think you pointed out earlier, the relationship is linear, meaning that the limiting case of a massless wheel would require no force to make a precession. This seems sort of intuitive.
gauss
