# What is centripetal acceleration

1. Jul 24, 2014

### Greg Bernhardt

Definition/Summary

Centripetal acceleration of something moving in a circle is the component of its acceleration towards the centre of the circle.

Equations

$$a_c=-\omega^2 r$$

$$a_c=-\frac{v^2}{r}$$

These apply if m and r are fixed, and even if $\omega$ and v are not.

The minus sign shows that the acceleration is towards the centre (in the opposite direction to increasing r).

Extended explanation

Centripetal acceleration is a fact of geometry, not of physics.

"Centripetal" means "seeking the centre" … it comes from the Latin word peto (I seek) … as does "petition".

It is used in physics, in combination with Newton's second law, to find the motion of an object which is obliged to follow a curved path.

A rotating (and therefore non-inertial) observer may invent a centrifugal force so that Newton's first law is true.

In exam questions, for example, it is used to solve problems about rollercoasters or about objects moving on the end of a string.

A car will lose contact with a rollercoaster when the reaction force between it and the rollercoaster is zero. By Newton's second law, the centripetal acceleration, A, times the mass, m, equals the normal component of the weight, mg, plus (or minus) the reaction force, and so the reaction force is zero when A = g cosθ, where θ is the angle between the rollercoaster and the horizontal.

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