The Relationship

Centripetal force (Fc) is directly proportional to the square of the angular speed (ω). This means:

* If you double the angular speed, the centripetal force increases by a factor of four (2²).

* If you triple the angular speed, the centripetal force increases by a factor of nine (3²).

The Formula

The formula for centripetal force is:

Fc = mω²r

Where:

* Fc = centripetal force

* m = mass of the object

* ω = angular speed

* r = radius of the circular path

In Summary

The centripetal force increases proportionally to the square of the angular speed.