Friction as Centripetal Force
Simple Explanation
When a car turns on a flat road, there is no string and no obvious inward force — but friction between the tyres and the road pushes sideways on the car, toward the centre of the turn, and that friction is what supplies the centripetal force.
Why Do We Need It?
Friction has a maximum possible value before tyres start to slide — this sets a real speed limit for how fast a car can safely take a given curve, which is exactly why sharp bends have lower speed limits than gentle ones.
See It
A diagram showing a car on a circular path with a red arrow labelled Friction pointing inward toward the centre of the turn
Formula
Centripetal Force (from speed)
Fc = mv² / r
The net force needed to keep a mass moving on a circular path of radius r at speed v.
- Fc
- — centripetal force, in newtons (N)
- m
- — mass of the object, in kilograms (kg)
- v
- — linear (tangential) speed, in metres per second (m/s)
- r
- — radius of the circular path, in metres (m)
When to use it: Whenever you know an object's linear speed and the radius it curves around, and need the net inward force.
Worked Example
Find a car's maximum safe turning speed
A 1000 kg car turns on a flat road of radius 50 m. The maximum friction available between tyres and road is μ = 0.4 (take g = 9.8 m/s²). What is the maximum safe speed?
Why Does This Work?
Friction can only push up to a maximum value, μ times the normal force, before the tyres lose grip and slide. As long as the centripetal force needed (mv²/r) stays below that maximum, friction supplies exactly what's needed — but push the speed higher and the car skids outward.
Real-Life Example
Icy roads and speed limits
The same curve becomes far more dangerous to drive around in icy conditions.
Ice drastically lowers μ, which lowers the maximum available friction — and therefore the maximum safe turning speed — which is exactly why icy bends cause so many skidding accidents at speeds that would be perfectly safe on dry tarmac.
Practice
A 800 kg car turns on a flat road of radius 20 m with μ = 0.5 (g = 9.8 m/s²). What is the maximum safe speed, in m/s?
HardCommon mistake
Forgetting that friction has a maximum limit — assuming friction can simply supply whatever centripetal force is needed at any speed, when in reality going too fast for the available friction causes the tyres to slide and the car to skid outward off its curved path.
Quick Review
- Friction supplies the centripetal force for a car turning on a flat road.
- Maximum available friction: Fmax = μmg.
- Maximum safe turning speed: v_max = √(μgr).