A centripetal force is a force 'towards the centre', causing circular motion. The acceleration corresponding to a centripetal force is called centripetal acceleration.
Any moving body that is not moving in a straight line is accelerating. This somewhat counterintuitive statement is a result of the definitions of velocity and acceleration. Both velocity and acceleration are vector quantities, meaning that they have both a magnitude and a direction. The acceleration of a body is the vector rate of change of its velocity, so if the direction of the velocity changes, there will be a corresponding acceleration. It can be shown that if the magnitude of the velocity does not change, then the acceleration is directed perpendicular to the direction of the velocity. .
If the acceleration, and thus the force, remains perpendicular to the velocity, then the body will move uniformly in a circle and the force is called a centripetal force. (If it doesn't, the perpendicular component of the force is still called the centripetal force, see radius of curvature for details) For a circular orbit of radius r, the required centripetal force is F = >em>mv2/r. This force is often provided by a central force such as gravity or electrostatics.
One context where centripetal force is often referred to is in connection with centrifugal force. As pedants everywhere are fond of pointing out, centrifugal force is not a 'real' force. The real force in that situation is a centripetal force. Centrifugal force is experienced as an inertial resistance to the centripetal force, making it an 'effective force' or pseudo force. In the reference frame of the body in circular motion, the centrifugal force appears as real as any other force. This is the cornerstone of all artificial gravity methods involving spinning bodies, familiar to fans of Ringworld and Babylon 5. One might ask where the centripetal force comes from for a rigid ring (or hollow cylinder) spinning uniformly around its centre. The answer is that the internal forces maintaining the rigidity of the body supply the centripetal acceleration, the alternative being the disintegration of the body with its pieces leaving along tangential paths.
In conclusion, the concept of centripetal force is central to any dynamical treatment of rotational motion.
This writeup is copyright 2003-2004 D.G. Roberge and is released under the Creative Commons Attribution-NoDerivs-NonCommercial licence. Details can be found at http://creativecommons.org/licenses/by-nd-nc/2.0/ .