Question

Mand show that theobtain an expression for the angle which a cyclist will have to make with the vertical while taking a circular turn ​

Answer 1

To provide the needed centripetal force, the cyclist will make an angle ∅ with the ground in reaction R. The reaction R will be a force acting on the cyclist at an angle ∅ to the vertical.

So, the vertical component R cos ∅ that has been made by the normal reaction R will help in balancing the weight mg of the cyclist. So, the horizontal force indicated by R sin ∅ will provide the cyclist with all the needed centripetal force.

The picture has been attached to show the detailed angles.