What is angle of banking? Obtain the condition for equilibrium of a body negotiating a smooth banked road.

When the outer part of the road is raised little above the inner part, to take the turn along the circular track, it is called banking of road.
The angle that the inclined track makes with horizontal is called angle of banking.
Consider a vehicle of weight mg mving around a banked curved track of radius r and inclination θ with speed v.


The vehicle is under the action of following forces:
(i) The weight mg acting vertically downward.

(ii) The reaction R of the track to the vehicle is acting perpendicular to banked track in upward direction.
The components of R is resolved into it's components.
The vertical component Rcosθ of normal reaction R will balance the weight mg of the vehicle.
The horizontal component R sinθ will provide the necessary centripetal force to the vehicle.
i.e.                                 ...(1)

and
                                     ...(2) 
Dividing (2) and (1),
                 
                   
The above equation gives the angle of banking.