^Bending while turning

If anything is pressed straight down, its reaction is straight up & has no horizontal component. But if pressing is done at some angle, then the reaction force has both horizontal & vertical components.

This trick is the basis of bending while turning of a bike, aircraft, ice skater etc.

The vertical component of the reaction of the pressing force balances the weight of the system

i.e.  mg = Ncosθ

The horizontal component of the reaction of the pressing force provides centripetal force helping him to take turn (change the direction)

Dividing the two equations we can say that the required angle of bending of cyclist is