# What would the period of rotation of Earth have to be for objects on the equator to have a centripetal acceleration with a magnitude of #9.80# #ms^-2#?

##### 1 Answer

Fascinating question! See the calculation below, which shows that the rotational period would be

#### Explanation:

To answer this question we need to know the diameter of the earth. From memory it's about

The centripetal acceleration is given by

Remember that we know the acceleration we want and the radius, and need to know the period of rotation. We can start with the rotational velocity:

To find the rotational period, we need to invert this to give

This yields

We can divide this by 3600 to convert to hours, and find