At a recent family gathering, the subject of centripetal force came up. One family member insisted that centrifugal force does not exist, and that centripetal force is the only force (in this context). This member insisted that when people generally refer to centripetal force, they are in fact wrong and that they should really be saying centripetal force instead. Two other opposing family members insisted that centrifugal force is the force imposed AWAY from the center, and that it opposes centripetal force that imposes a force TOWARD the center. Kind of a “you cant have one without the other” type of thing.
Centrepetal force is the force required for any body to follow a circular path. So if u take a rock, tie it to the string and swirl it around, the centripetal force (the tension in the string) is keeping the rock in its path. You provide this tension to the string, which is the centripetal force. Now another way of looking at it would be that the rock is pulling at u - so the rock is exerting the force on you in which case you will call it centrifugal force.
Centrifugal force is sometimes called a pseudo force, because it arises from choosing your reference system (the rotating body).
PS : Newtons laws are not valid in non Inertial system (the rotating body being such a system.)