# Formula Circular motion Centripetal acceleration Velocity Radius

## Centripetal acceleration

`\( a_{\text z} \)`Unit

`\( \frac{\mathrm{m}}{\mathrm{s}^2} \)`

It is the acceleration experienced by a body (e.g. a planet, a particle) moving on a circular path. The centripetal acceleration points like the centripetal force to the center of the circle (in radial direction).

The centripetal acceleration is larger, the larger the velocity \(v\) of the body and the smaller the radius \(r\) of the circular orbit.

For example, if a body with \(v = 2 \, \frac{\mathrm m}{\mathrm s} \) moves on a circular orbit with radius \(r = 1 \, \mathrm{m} \), then this body experiences the following centripetal acceleration:`\begin{align}
a_{ \text z } &~=~ \frac{(2 \, \frac{\mathrm m}{\mathrm s})^2}{ 1 \, \mathrm{m} } \\\\
&~=~ 4 \, \frac{\mathrm m}{\mathrm{s}^2}
\end{align}`

## Velocity

`\( v \)`Unit

`\( \frac{\mathrm m}{\mathrm s} \)`

Velocity of the body moving in a circle.

## Radius

`\( r \)`Unit

`\( \mathrm{m} \)`

Radius of the circular trajectory. This is the distance from the center of the circle to the orbiting body.