I have been studying Irodov's problem book. There are a lot of good problems that challenge conceptual knowledge, and so I have to ask somebody for a qualitative answer. I can best describe my confusion by example, so let's take problem 1.284:
We have a gyroscope precessing around it's vertical axis (Figure 1.73). The axis of the gyroscope is horizontal.
I have managed to find an online solution here. So, since the gyroscope is rotating about it's symmetry axis, I agree that it will have angular momentum in the horizontal plane (it has a radial angular velocity).
However, it seems that this solution neglects the angular velocity of precession, as it relates to the angular momentum of the gyroscope. If the gyroscope is rotating in the horizontal plane, the precession angular velocity vector should point vertically. Shouldn't the gyroscope then have angular momentum in the vertical direction?
Is this maybe due to the referential frame (do we perhaps observe the gyroscope from a frame rotating vertically with angular velocity equal to the precession angular velocity)... ? If this is the case, why is there no centrifugal force?
Something doesn't add up, either way.