5.2 By banking of roads

1.1 Angular Variables
1.2 Kinematic equation for circular motion
1.3 Relation between angular and linear variables
1.4 Unit vectors along the radius and tangent
1.5 Velocity and acceleration of particle in circular motion

2.1 Centripetal force
2.2 Application of circular motion

3.1 Conditions for a particle in a circular motion

4.1 Conditions for a rod in a vertical circular motion

5.1 By friction
5.2 By banking of roads
5.3 By both friction and banking of road

Circular turn due to friction has speed restrictions i.e. $v \leqslant \sqrt {\mu rg} $.

Therefore, it is not always reliable at circular turns where vehicle is moving at high speed and where sharp turns are involved.

To avoid dependence on friction, the roads are banked at the turn so that the outer part of the road is some what lifted compared to the inner part.

When a jeep of mass $m$ runs on a circular track of radius $R$ which is banked at an angle $\theta $, the necessary centripetal force for circular turn is provided by the component of the normal force.

From FBD we get, $$\begin{equation} \begin{aligned} N\cos \theta = mg\quad ...(i) \\ N\sin \theta = \frac{{m{v^2}}}{R}\quad ...(ii) \\\end{aligned} \end{equation} $$

Dividing equation $(i)$ and $(ii)$ we get, $$\begin{equation} \begin{aligned} \tan \theta = \frac{{{v^2}}}{{Rg}} \\ v = \sqrt {Rg\tan \theta } \\\end{aligned} \end{equation} $$