Consider a cyclist of negotiating a curve of radius r with velocity 'v'
Weight of the cyclist, W=m g
In order to provide the necessary centripetal force, the cyclist leans through angle in inward direction as shown in figure above.
The various forces acting on the cyclist are:
(i) Weight Mg acting vertically downward at the centre of gravity of cycle and the cyclist.
(ii) The reaction R of the ground onto the cyclist, acting along a line, making angle with the vertical.
The cyclist while taking the turn is in equilibrium, therefore the vertical component Rcos of the normal reaction R will balance the weight of the cyclist.
The horizontal component Rsin will provide the necessary centripetal force to the cyclist.