Centripetal Acceleration
Simple Explanation
An object moving at constant SPEED in a circle is still accelerating, because its VELOCITY (which includes direction) is constantly changing direction. This acceleration always points toward the centre of the circle and is called centripetal ("centre-seeking") acceleration.
Why Do We Need It?
This is a common source of confusion in physics: 'constant speed' does not mean 'zero acceleration' when the direction is changing — recognising this is essential for correctly analysing any circular motion.
Formula
Centripetal Acceleration
a = v² / r
The acceleration directed toward the centre of a circular path, responsible for continuously changing the direction of an object's velocity.
- a
- — Centripetal acceleration, in m/s²
- v
- — Speed along the circular path, in m/s
- r
- — Radius of the circular path, in metres
When to use it: Use whenever an object moves at constant speed along a circular path and you need the acceleration causing that curved motion.
Worked Example
Calculating centripetal acceleration
A car takes a curve of radius 50 m at a constant speed of 15 m/s. Find its centripetal acceleration.
Why Does This Work?
Velocity is a vector — even at constant speed (magnitude), a continuously changing direction means the velocity vector is continuously changing, which by definition is acceleration. Careful geometric analysis of this changing direction shows the acceleration must point toward the centre, with magnitude v²/r.
Real-Life Example
Why cars can skid on tight curves
A car travelling too fast around a tight curve can skid off the road.
Centripetal acceleration increases sharply with speed (it depends on v²) and with tighter curves (smaller r) — if the required centripetal acceleration exceeds what friction between the tyres and road can provide, the car cannot maintain the curved path and skids outward.
Practice
An object moves in a circle of radius 2 m at 6 m/s. Find its centripetal acceleration.
MediumCommon mistake
Thinking constant speed means zero acceleration — in circular motion, the speed (magnitude) is constant, but the velocity (which includes direction) is always changing, so there is always a nonzero centripetal acceleration.
Quick Review
- Centripetal acceleration a = v²/r, always directed toward the centre.
- Constant speed in a circle still means nonzero acceleration, because direction is changing.
- Doubling speed quadruples the required centripetal acceleration (v² dependence).