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Bending of a Cyclist

Consider a cyclist of weight mg taking a turn of radius r with velocity v. In order to provide the necessary centripetal force, the cyclist leans through angle θ inward as shown in Fig. 4.
 
37488.png
Fig. 4
 
The cyclist is under the action of the following forces:
  • The weight mg acting vertically downward at the center of gravity of cycle and the cyclist.
  • The reaction R of the ground on cyclist. It will act along a line-making angle θ with the vertical.
  • The vertical component R cos θ of the normal reaction R will balance the weight of the cyclist, while the horizontal component R sin θ will provide the necessary centripetal force to the cyclist.
36970.png
 
Dividing (1) by (2), we have
 
36964.png
or 36958.png
 
Therefore, the cyclist should bend through an angle
 
36952.png
 
It follows that the angle through which cyclist should bend will be greater, if
  1. The radius of the curve is small, i.e., the curve is sharper.
  2. The velocity of the cyclist is large.
Note: For the same reasons, an ice skater or an aeroplane has to bend inwards, while taking a turn.




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