Question

Why we cant fall from a bicycle while it's running? What is the implicit physics?
Is there a numerical example?

Answer 1

It is easy to balance a bicycle when it is moving at a fairly high velocity, say 7 m/s or 25 km/hr. But when a bicycle slows down, it is hard to keep it upright, and the person riding it may thus fall down!

The most common explanation is that the wheels on a bike act as a gyroscope, preventing the bike from falling over. A bike was constructed with counter-rotating wheels to test this. The bike had two front wheels, one on the ground and rotating forward, and one off the ground rotating backward. This way, the total angular momentum was zero. However, the bike remained stable.

Another explanation is that the stability of the bike depended on the angle between the frame and the front wheel. Whenever the bike starts tipping to the side, the front wheel turns into the curve to counter-act the tipping. This was also tested by constructing a bike with the front fork going directly up. This also was stable, disproving this hypothesis.