Question

A rock in a sling is swung around in a circle. How would the centripetal force change if the rock was 9 times lighter?

Answer 1

The force would be `1/9th` of that required to spin the larger rock at the same speed.

Explanation:

The force required for angular acceleration is proportional to the mass and the rate of acceleration.
`F = ma`
In this case we usually know either an angular speed (`omega`) or an instantaneous velocity (`v`) and a radius (`r`). So it's also correct to write either of these forms:
`F=mv^2/r`
`F=mromega^2`

In either case the force required changes in direct proportion to the mass. If `m=9` the force would be nine times larger than the case where `m=1`.