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.
Boomer Biker tries to get it right, but ends up in a muddled mess anyway, with statements such as these:
“Gyroscopic precession” is the tendency of a rapidly spinning object to resist being tilted.
Precession is far more powerful than gyroscopic stability.
Oddly, the first statement is immediately followed by a dictionary definition which contradicts it.
The second statement is one of several that invokes “gyroscopic stability” as though it were some phenomenon different from precession.
What appears to be stability is exactly precession. Spinning objects respond to an applied torque by rotating about a third axis, perpendicular to both the spin axis and the axis of the applied torque and at a rate inversely proportional to the spin rate. That is all. If a gyroscope or a spinning bike wheel is prevented from precessing, as the rear wheel of a bike usually is, it moves in response to an applied torque exactly as it would if it were not spinning. There is no magic stability.
Professor Cossalter, on page 304 of the second edition of his in his excellent Motorcycle Dynamics, calculates the roll moment generated by gyroscopic effect for a motorcycle traveling at 22 m/s (79 km/h or 49 mph) to be 3.5 N-m (2.6 lb-ft) and compares it to the roll moment generated by the accelerating contact patches of 30 N-m (22 lb-ft), which is 8.6 times larger. He concludes with the note that the gyroscopic effect is present from the instant torque is applied at the handlebars, and the roll moment generated by the lateral force of the tires can take some time, ~0.1 seconds in this example, to build up.