Uniform Circular Motion

Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle.

Uniform circular motion

When an object is experiencing uniform circular motion, it is traveling in a circular path at a constant speed. If r is the radius of the path, and we define the period, T, as the time it takes to make a complete circle, then the speed is given by the circumference over the period. A similar equation relates the magnitude of the acceleration to the speed:

                   

These two equations can be combined to give the equation:

This is known as the centripetal acceleration; v2 / r is the special form the acceleration takes when we’re dealing with objects experiencing uniform circular motion.

A warning about the term “centripetal force”

In circular motion many people use the term centripetal force, and say that the centripetal force is given by:

I personally think that “centripetal force” is misleading, and I will use the phrase centripetal acceleration rather than centripetal force whenever possible. Centripetal force is a misleading term because, unlike the other forces we’ve dealt with like tension, the gravitational force, the normal force, and the force of friction, the centripetal force should not appear on a free-body diagram. You do NOT put a centripetal force on a free-body diagram for the same reason that ma does not appear on a free body diagram; F = ma is the net force, and the net force happens to have the special form  when we’re dealing with uniform circular motion.

The centripetal force is not something that mysteriously appears whenever an object is traveling in a circle; it is simply the special form of the net force.