a wheel spins around the Y axis, gravity applies and the upper part starts spinning around the Z axis. The textbook explained this with angular momentum, looks simple, but it is really weird when I try to think about this in other ways. Usually when i see something start spinning, i think there is an force pushing it, but in this case I can't find such a force. There is a kind of gap in my head, and it really disturbs me. Please help me.
You have my sympathy; precession is little understood. Try it this way!
i) remove the front wheel from a bicycle and mark a spot on the tyre.
ii) hold it by the ends of the axle between your hands with the mark at "top dead centre".
iii) set the wheel spinning as though the machne was progressing forward (very slowly)
Note that the spot travels forward and downards
iv) Rotate the axle in the horizontal plane - right hand toward you , left hand away (imitate turn to the right).
v) NOW that spot is rquired to move forward but to combine its downward motion with a motion to the right?
vi) There is only one possible way to achieve this result and that is for the axle to rotate in the vertical plane - right-hand upward and left-hand downward.
THIS IS THE MOTION OF PRECESSION
Spin in plane A
Compell rotation in Plane B
Resulting motion is largely in PlaneC.
This becomes very interesting (for sadomasochists) when two such spinning wheels are coupled by a rigid frame (e.g. a bicycle).