# Why don’t you fall when you lean on a bike while it turns?

Let’s say you’re on a bike and you turn left and also lean left with it. As we know fron experience you remain stable. How is this? There is obviously a torque caused by gravity at the center of mass around the pivot point(wheel ground contact point). If we instead take the center of mass as the pivot point it has a torque in the opposite direction caused by the wheel friction force radially inwards. Can anyone clarify this?

• Imagine balancing a stick with a mass on the end, if the stick tilts, to balance it you would move the bottom of the stick toward where it is leaning to keep it stable, this is the same principle , there are equal and opposite torques when this happens Commented Aug 4, 2023 at 15:48
• An answer in slightly over one minute - The Counterintuitive Physics of Turning a Bike and there are many other gems at minutephysics. Commented Aug 4, 2023 at 16:43
• A classic example of something that is far easier to do than it is to explain. ;-) Commented Aug 4, 2023 at 17:46

The condition that no rotation means no net torque is not guaranteed to be true when the object is accelerating and you consider a point other than the center of mass. So when you use the contact point as the axis they don't sum to zero. This is because the non-zero net torque is causing a change in the vehicle's angular momentum. But instead of a rotation, it's a linear acceleration.

If we instead take the center of mass as the pivot point it has a torque in the opposite direction caused by the wheel friction force radially inwards.

There are two forces from the ground, the friction pointing inward, and the normal force pointing upward. Together these should sum to zero torque about the center of mass.

to turn left, you first steer slightly to the right. this places your center of support to the left of your center of mass and you start to fall to the left. then you turn to the left to "follow" the track taken by your front wheel and to halt the fall. when you have turned as far as you want, you then steer to the left to bring the center of support back underneath your center of mass and you return to an upright position.

You perform all of these maneuvers without conscious thought.

The description above holds true for when you are cruising at speed. When you are moving very slowly, you stay upright by manually forcing the handlebars left and right to "teeter" yourself out of a fall, and you change direction by biasing those handlebar swings in one direction.

Between those extremes, you use a combination of the two techniques.

This topic is a solved problem in the engineering field of tracking vehicle dynamics.