# Centripetal force and acceleration

The centripetal force is the force which is **perpendicular** to the direction of motion of an object undergoing circular motion.

It points to the **centre** of the circle, and is responsible for **changing the direction** of the velocity.

It is often confused with the **centrifugal force**, which is the **reaction force** that points outwards from the centre of rotation (opposite to the centripetal force).

The centrifugal force is considered to be a "fictitious force" as it only acts in the frame of reference of the object.

The centripetal force does not refer to a specific type of force like tension, friction or gravitation. The type of centripetal force will be different depending on the situation.

Situation | Type of centripetal force |
---|---|

Planet orbiting sun | Gravity |

Ball swung on string | Tension |

A simple expression for the **magnitude of centripetal force** follows from Newton's second law:$$$\begin{align*}F=ma=\frac{mv^{2}}{r}=mr\omega^{2}\end{align*}$$$The variable $$a$$ is the magnitude of centripetal acceleration (i.e. acceleration directed towards the centre). It is given by:$$$\begin{align*}a&=\frac{v^{2}}{r}=r\omega^{2}\end{align*}$$$

$$v=$$linear speed; $$\omega=$$angular speed; $$r=$$radius of circular motion.