why don't centripetal and centrifugal force cancel each other?

 Centripetal and centrifugal are the two forces used to analyze circular motion, but both act in opposite directions and so many of us think they should cancel each other. This is the question that is going to be answered in this post.

Centripetal force is necessary to keep a particle in circular motion, and it only acts on a particle that is moving in a circle.

On the other hand centrifugal force is a pseudo force that acts in the frame of reference of the particle moving in a circle or an observer moving with it. 

If we consider a bus that is moving in a circle then in the frame of reference of the passengers a centrifugal force will act in the direction away from the center, but in the frame of reference of passengers centripetal force wouldn't exist as they wouldn't observe the bus to move in a circular path.

In a similar fashion for an observer observing from the ground, a centripetal force will act on the bus pulling it towards the center but since centrifugal force only applies for non-inertial frames, it wouldn't exist for the observer on the ground as it is observing from an inertial frame.

So, that's why centripetal force and centrifugal force don't cancel each other, as only one exists for a given observer.

THANKS FOR READING!!

-Arvin Gupta