While driving along an unbanked circular road, a two-wheeler rider has to lean with the vertical. Why is it so? With what angle the rider has to lean? Derive the relevant expression. Why such a leaning is not necessary for a four wheeler?
Answers
A rider must lean into a turn to prevent tipping over in the other direction. To remain upright while turning to the left, there are three forces acting on the rider and bicycle.
The weight of the rider and bicycle, W, acts vertically downward from their center of gravity. The normal force, N, of the road acts vertically upward from a point below the center of gravity. And the frictional force, F, of the road acts horizontally to the left. Turning on a bike requires a net force called centripetal force. The frictional force provides the centripetal force necessary to turn the cyclist to the left. But the frictional force also produces a clockwise torque that will cause the rider and bicycle to tip clockwise to the right. In the sketch on the right the cyclist is leaning in the direction of turn. Now the normal force of the road does not act through the center of gravity. It produces a counterclockwise torque that cancels out the clockwise torque of the frictional force. Thus there is no tendency for the cyclist to tip to the right.