Centripetal force

The centripetal force is the force that causes an object to move in a circle, acting towards the centre of the circle. In the case of a satellite the centripetal force is gravity, in the case of an object at the end of a rope, the centripetal force is the tension of the rope.

It is important to understand right from the start that there is no 'default', 'natural' centripetal force. By default, objects tend to move in a straight line, as Newtonian mechanics teaches, away from the 'orbit', so in this context, by default there is only a centrifugal force at work. The centripetal force is being applied either by accident (meteors orbiting a planet) or artificially (satellites orbiting Earth, the object at the end of a rope etc). Therefore, the centrifugal force is a natural component of a circular movement, while the centripetal force is what we conventionally call the force keeping the object 'in orbit'.

Objects moving in a straight line with constant speed also have constant velocity. However an object moving in an arc with constant speed has a changing direction of motion. As velocity is a vector of speed and direction, a changing direction implies a changing velocity. The rate of this change in velocity is the centripetal acceleration. Differentiating the velocity vector gives the direction of this acceleration towards the centre of the circle. By Newton's second law of motion, as there is an acceleration there has to be a force in the direction of the acceleration. This is the centripetal force, and is equal to: