Physics · Laws Of Motion · NEET
On a flat road, only friction between tyres and road supplies the centripetal force needed to turn. Friction is limited and drops in rain or on worn tyres, so a fast turn can skid. Banking tilts the road so the normal reaction N leans toward the centre. The inward component N sinθ now helps provide the centripetal force. This means the car can turn at higher speed with less reliance on friction, which is safer.
No. Even on a frictionless banked road a car can still turn if it moves at the ideal (design) speed. Setting friction μ = 0 in the equations gives tanθ = v²/(Rg), so the ideal speed is v = sqrt(gR tanθ). At this exact speed the tilt alone supplies all the centripetal force, so tyres feel no sideways friction and wear is minimum. Friction only becomes necessary when the car goes faster or slower than this ideal speed.
When the car is at its highest safe speed it tends to slide outward and up the slope, so friction acts DOWN the incline (toward the centre side). Balancing forces gives N cosθ = mg + μN sinθ (vertical) and N sinθ + μN cosθ = mv²/R (centripetal). Dividing the two removes N and m: v²/(gR) = (tanθ + μ)/(1 − μ tanθ). So v_max = sqrt(gR(tanθ + μ)/(1 − μ tanθ)). Notice the mass cancels, so the answer never depends on the car's mass.
The normal reaction is always perpendicular to the surface, not perpendicular to the horizontal ground. When the road is tilted by angle θ, the whole surface tilts, so N tilts by θ too. Its vertical component N cosθ balances gravity, and its horizontal component N sinθ points inward toward the centre of the circle, which is exactly what centripetal motion needs. This tilt of N is the key idea the derivation uses.
A car is negotiating a curved road of radius R. The road is banked at an angle θ and the coefficient of friction between the tyres and the road is μs. The maximum safe velocity on this road is:
A car travels on a circular racetrack of radius 50 m, banked at angle θ. If the car travels at a speed 10 m/s, the wear and tear on its tyres is minimum. Taking g = 10 m/s², the value of θ is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
v_max = sqrt(gR(tanθ + μ)/(1 − μ tanθ)), where R is the radius of the curve, θ is the banking angle and μ is the coefficient of friction. Mass does not appear.
The ideal or design speed is v = sqrt(gR tanθ), found by putting μ = 0. At this speed no friction is needed, so tyre wear is minimum. It follows from tanθ = v²/(Rg).
At maximum speed the car tends to slip outward and up, so friction acts down the slope (toward the centre). At minimum speed it tends to slip inward and down, so friction acts up the slope. At the ideal speed friction is zero.
No. The mass m cancels during the derivation, so maximum safe speed depends only on g, R, θ and μ. A truck and a car have the same safe speed on the same banked curve.
Banking is a fixed application of circular motion in the Laws of Motion chapter, and NEET has repeatedly asked its formula (2016) and the minimum-wear ideal-speed idea (ReNEET 2026). Knowing the derivation lets you answer both direct-formula and conceptual questions quickly.
