Circular motion
 The work of a curious fellow

When what goes around comes around...
 Imagine that a particle is subject to a force of constant magnitude but whose direction may change. The particle's acceleration at any instant would be in the direction of the force at that instant. The change in the particle's velocity over a very short time would be a vector in the direction of the average acceleration. The new velocity at the end of this tiny time interval would be the vector sum of the original velocity and the change in velocity. The displacement of the particle during the little time slice would be given by the average velocity times the Dt. Now suppose that the changing direction of the force was such that the force was always perpendicular to the velocity. The Central Force display illustrates this situation. Notice that in this example that the force bends the path of the particle into a circle and that the force vector and therefore the acceleration always points toward the center of that circular path. The magnitude of the velocity along the path remains constant. Under these conditions the particle is said to be undergoing uniform circular motion where "uniform" means the speed of the particle is constant. We have evidently caught this system in a delicate balance where in each Dt the force deflects the particle just enough from the trajectory it would have followed, a straight line in the direction of the velocity, that it ends up on a circular path. The question now is what must be the relationship among the acceleration, velocity and radius of the circle for us to get this nice result.