Beware that there is no such thing as centrifugal force! Centrifugal means "center-fleeing". The term centrifugal force is the result of misconception based on common sense. Common sense is a disaster in Physics, so beware!
An object undergoing circular motion is not moving along a straight line, it's moving in a circle and therefore the direction of its velocity is continuously changing. If there was a centrifugal force (outward force), the net force would be zero and the body must move in straight line (according to Newton's first law).
The expression \(mv^2/r\) for centripetal force is not a force, it is equal to the force but not the force itself (it means it is the same as \(m\vec a\) part in Newton's second law not part of the \(\sum \vec F\).) You need to review Newton's second law where we pointed out \(m \vec a\) is not the force!
There are some common misleading events that make you think about the existence of centrifugal force. You move outward while turning your car away from the center of the curve made by the turn. In this case the car made the turn not you. You were moving in straight line and you want to keep that straight-line motion and when the car turns it seems like the you are moving outward (review inertial frame of reference).
Another misconception may arise when you swing a ball attached to a string. You apply force on the string to keep the ball swinging and the ball also exerts equal magnitude of force back on you (review Newton's third law) and you end up thinking the force exerted by the string on you is also being exerted on the ball outward!
If there is a thing like centrifugal force, the ball should move outward from the circular path not along the tangential line when the string breaks. This is clearly illustrated by Figure 1. Centrifugal force is a mistake, and we never ever think about it again.
