After a great start, with correct statements such as
bikes are, however, dynamically stable, or stable when moving forward, because steering allows a rider to move the bike’s points of support around under the center of gravity and keep it balanced,
the wheels come of the cart in paragraph 3 with this mess:
Spinning wheels have angular momentum, and when you’re sitting on a bike, you and it and its wheels make up a system that obeys the principle of conservation of angular momentum. Unless torque, or twisting force, is applied from outside the system to change the wheels’ angular momentum, that momentum and the direction of the momentum remain constant. In a nutshell, once the wheels line up a certain way, they want to stay lined up like that. It’s easy for you to move them, but hard for an outside force to do the same, and so the bike is easy to keep balanced but doesn’t topple easily.
1. Unless you and your bike are in free fall in a vacuum, angular momentum will not be conserved. The slightest lean will allow gravity and the ground contacts to form a couple that applies a large external moment to the system.
2. The wheels do not care which way they are lined up and will easily change orientation in response to external torques, such as the roll torque described in point 1 above or a steering torque.
The rear wheel is generally prevented from presessing in response to a rolling moment, and so will roll with the rear frame exactly as if it were not spinning at all.
The front wheel is generally free to rotate about the steering axis and so gyroscopic pressession will cause it to steer in the direction of an applied roll torque and lean opposite to the direction of the applied steer torque.
It pains me a little to point out this flaw because the article ends with a plug for the wikipedia article and even credits me for the picture I downloaded from elsewhere on wikipedia and cropped to show cyclist performing a track stand, but facts is facts, and this article gets a couple of key facts wrong.