Unfortunately, inspite of our feelings, there is no such thing. It's false, it's non-existent, and you will never feel it. When you go round a circle in a roller coaster or merry go-round, there is no force pushing you radially outward, rather, by Newton's 1st law, you have a tendency to fly tangentially, as that is the direction of the velocity with which you will continue if there was no force. In fact, if there was a centrifugal force, you can never go round in a circle, you will continually get thrown radially out, not tangentially.
So what causes you to go round a circle, for if there was no force, you will surely continue on the tangential path? And what is the push you feel in a circular path? That is the tricky centripetal force. Actually, there no trick to it. The railing of a merry-go-round or the seat in a roller coaster pushes you inwards, towards the center of the circle, so that you don't fly off at a tangent, rather, as a result of the force, you accelerate towards the center. That is not to say you quickly make a bee-line to the center, rather, your motion gets a radial acceleration so the direction of the velocity changes a little towards the center and you land up in a circular path.
Makes sense?
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