The bicycle wheel article on the award-winning HyperPhysics website runs into trouble immediately, in the first sentence:
The angulur momentum of the turning bicycle wheels makes them act like gyroscopes to help stabilize the bicycle.
It later tries to temper that bold assertion with a disclaimer,
it should be pointed out that experiments indicate that the gyroscopic stability arising from the wheels is not a significant part of the stability of a bicycle,
but the damage is already done. We can allow that the gyroscopic pressesion of the front wheel does contribute to it steering in the right direction to correct for a lean, but that still leaves the rear wheel, which is the only possible interpretation of the plural “wheels”.
The rear wheel is prevented from precessing by the rear frame, which is in turn prevented from yawing by the contact patches of the two wheels, and when a spinning object is prevented from precessing, it reacts to an applied torque exactly as it would if it were not spinning at all. Thus the angular momentum of the turning rear wheel is no help at all in stabilizing a bicycle or a motorcycle.