Centripetal Force
Simple Explanation
A centripetal force is the net force that keeps an object moving along a circular path. It always points toward the centre of the circle — never forward, never outward — which is exactly why it's called centripetal, from Latin for 'centre-seeking.'
Why Do We Need It?
Newton's first law says an object keeps moving in a straight line unless a force acts on it. A centripetal force is what continuously bends that straight-line path into a circle — without one, anything moving would simply fly off straight.
See It
A diagram showing an object on a circular path, with a red arrow labelled Fc pointing inward toward the centre and a blue arrow labelled v pointing tangent to the circle
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 the centripetal force on a swung ball
A 0.5 kg ball on a string moves in a circle of radius 0.8 m at a constant speed of 4 m/s. Find the centripetal force acting on it.
Why Does This Work?
An object moving in a circle is constantly accelerating toward the centre — even at constant speed — because its direction keeps changing. This centripetal acceleration equals v²/r. By Newton's second law (F = ma), the net force producing that acceleration must be F = mv²/r.
Real-Life Example
A car going around a roundabout
A car drives around a roundabout at a steady speed.
Friction between the tyres and the road supplies the centripetal force that continuously turns the car's straight-line motion into the curve of the roundabout.
Practice
A 2 kg object moves in a circle of radius 5 m at 10 m/s. What centripetal force acts on it?
MediumCommon mistake
Treating centripetal force as an extra force added on top of gravity, tension, friction, or the normal force — it isn't a new force at all. It's just the name for whichever real force (or combination of real forces) happens to point toward the centre and keep the object turning.
Quick Review
- Fc = mv²/r — the net inward force needed for circular motion.
- Centripetal force always points toward the centre of the circle.
- It is not a separate force — it's supplied by tension, friction, gravity, or the normal force.