Motion of Vehicle on a Plane on a Circular Path
A circular turn on a level road : Consider a car of weight ‘mg’ going around on a circular turn of radius ‘r’ with velocity non a level road as shown in the figure. While rounding the curve, the wheels of the vehicle have a tedency to leave the curved path and regain the straight line path.
Force of friction between the wheel and the road opposes this tendency of the wheel. Therefore, this frictional force acts towards the centre of the circular path and provides the necessary centripetal force.
Three forces are acting on the car Figure.
(i) The weight of the car, mg, acting vertically downwards,
(ii) Normal reaction N of the road on the car, acting vertically upwards,
(iii) Frictional force F, along the surface of the road, towards the centre of the turn,
As there is no acceleration in the vertical direction,
N – mg = 0
or N = mg ……….. (i)
Since, for safe driving of a car, on the circular path, the centripetal force must be equal to or less than friction force.
Here, μ is coefficient of static friction between the tyres and the road.
Hence, the maximum velocity with which a vehicle can go round a level curve; without slidding is
v = \(\sqrt{\mu r g}\)
The value of v depends upon :
(i) Radius r of the curve.
(ii) Coefficient of friction (μ) between the tyre and the road.
Clearly v is independent of the mass of the car
