Question

A rock in a sling is swung around in a circle. How would the centripetal force change if the rock was swung 5 times faster?

Answer 1

It would increase 25 times.

Explanation:

The rock is undergoing centripetal acceleration of magnitude `a_c=v^2/r` and directed towards the centre of the circle.

By Newton's 2nd Law of motion, the resultant centripetal force required to achieve this is given by `sumF=ma_c=(mv^2)/r`.

So if the velocity of swing is increase 5 times, it implies that `v^2` will increase `5^2=25` times and hence the centripetal force `F_c` will also increase 25 times in order to keep it in a circular motion.