5.1 By friction

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

Let a jeep of mass $m$ is running at speed $v$ on a horizontal circular arc of radius $R$, the frictional force $f$ acting between the tires and ground will provide necessary centripetal force to the jeep.

Coefficient of friction between the jeep tires and road is $\mu $.

Limiting frictional force $\left( {{f_L}} \right)$ is,

$${f_L} = \mu N$$

From the FBD we get, $$\begin{equation} \begin{aligned} N = mg \\ f = \frac{{m{v^2}}}{R} \\\end{aligned} \end{equation} $$

So, the friction $f$ provides the necessary centripetal force for turning.

If the velocity $v$ of the jeep is more, centripetal force increases which in turn increases the frictional force.

$v=v_max$ is the maximum speed at which the jeep can take the safe turn.

So, at this speed maximum frictional force acts between the tires and the ground i.e. limiting frictional force.

$$\begin{equation} \begin{aligned} {f_L} = \frac{{mv_{\max }^2}}{R} \\ \mu mg = \frac{{mv_{\max }^2}}{R} \\ {v_{\max }} = \sqrt {\mu gR} \\\end{aligned} \end{equation} $$

Note: If $v > \sqrt {\mu gR} $, the car will slide outwards as $v \propto R$.