Simulation · Physics · Class 11

What keeps a car on a banked curve

From the lesson Circular motion in Laws of Motion. Change the values and watch what happens.

The idea behind it

NCERT § "Circular Motion"

Moving at speed v in a circle of radius R, a body has an acceleration v²/R directed towards the centre, so it needs a net force mv²/R towards the centre.
Centripetal force is not a new kind of force; it is supplied by an existing force such as tension, gravity, or friction.
On a level (unbanked) road the centripetal force comes only from static friction between tyres and road, giving a maximum safe speed v_max = √(μ_s R g), independent of the car's mass.
Static friction, not kinetic, is used here because the tyres do not slip sideways on the road.
On a road banked at angle θ, a component of the normal force also points towards the centre, raising the maximum safe speed.
At the optimum speed v₀ = √(R g tan θ) the normal force alone supplies the centripetal force and friction is not needed, which reduces tyre wear.
Below the optimum speed friction acts up the slope; above it, friction acts down the slope.

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