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Centripetal acceleration
Intermediate
Acceleration directed to the centre of the circle.
a = v²/r = ω²rThe acceleration toward the centre is a = v²/r = ω²r. It changes direction, not speed. It is provided by a real force such as tension, gravity or friction.
At 20 m/s on a 100 m curve: a = 4 m/s².
Centripetal acceleration is a result, not an additional force on the free-body diagram.
In more detail
Centripetal acceleration is a = v²/r = ω²r, directed towards the centre of the circle. It is the acceleration needed to keep an object moving in a circle.
Real-world uses
- Designing roads and rides so passengers feel a comfortable centripetal acceleration.
- Calculating the acceleration of a ball on a string swung in a circle.
- A car taking a bend feels pushed outwards, while in fact the friction of the tyres supplies the inward centripetal acceleration.
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Frequently asked questions
Is centripetal acceleration a new kind of force?
No. It is provided by real forces such as tension, friction or gravity, which point towards the centre.
What happens if the centripetal force disappears?
The object moves off in a straight line, tangent to the circle.
Does centripetal acceleration do work?
No. It points towards the centre, perpendicular to the velocity, so it changes the direction of motion but not the speed.
Related topics in Kinematics
Uniform circular motion · Angular displacement and velocity · Period and frequency · Non-uniform circular motion · Angular acceleration · Rotational kinematics equations