IIT (NTSE/Olympiad)  

Circular Motion & Rotational Dynamics

9. Banking of Tracks

9. Banking of Tracks
When a vehicle moves round a curve on the road with sufficient speed, there is a tendency of over turning for the vehicle. To avoid this the road is given a slope rising outwards. The phenomenon is known as banking
(i) Let there be vehicle on a road having slope θ. R = normal reaction of the ground
Horizontal component Vertical component
R sin θ
It provides necessary centripetal force
R sin θ =
R cos θ
It balances the weight of the vehicle
R cos θ = mg

⇒ tan θ = v2/rg
This equation gives the angle of banking required.

IIT (Class X)