This explains why we can ride a bicycle without falling. As we pedal forward, the angular momentum vector of the wheels points straight to our left. Put your right fingers in the direction of the wheels. Your thumb will point to your left, which is the direction of the angular momentum.

 

What happens as we lean to the left? If the bicycle were stationary, we would fall. The angular momentum of our falling would point to the rear. (Hold your fingers in the direction of the fall. The thumb would point in the direction of the angular momentum.) This is because the torque of gravity points to the rear. However, when we are riding and lean to the left, the torque of gravity causes the angular momentum L to change by ΔL, which points to the rear. Adding L and ΔL gives a vector pointing slightly to the rear – the bicycle turns to the left.

 

 

We hold the handlebars straight. Just by leaning our body to the left causes the bicycle to turn to the left. The only way to really understand this is by understanding cross products of vectors, angular momentum and torque.

 

This explanation is to my mind one of the most beautiful explanations in physics. Just by using mathematical ideas, we explain how riding a bicycle works!