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

Nov 4, 2015

The force would be $\frac{1}{9} t h$ 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.
$F = m a$
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:
$F = m {v}^{2} / r$
$F = m r {\omega}^{2}$

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 $m = 1$.