If an object moves in a circle it is accelerating and there has to be an unbalanced force acting on it. If, for instance, you tie a weight on a string and swing it around over your head in a circle you can feel the centripetal force needed to keep it going in a circle. If you let go, that is remove the centripetal force, it will fly off in a straight line in whatever direction it happens to be going at that moment. Centripetal acceleration is found using the following equation:

a_c = v² / r

The units are as follows: a_c - centripetal acceleration, v² - velocity squared of an object, r - radius of a circle around which an object is moving. What this means is that the weight is being pulled toward the center of its revolution by the forceapplied to it. It never gets to the center however. It has two motions. One is an acceleration toward the center and the other is a constant velocity perpendicular to that acceleration. At each instant in time it is moving toward the center and at the same time it moves away from it.