# 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:

$\large&space;\large&space;v=\frac{2\pi&space;r}{T}$                   $\large&space;a=\frac{2\pi&space;v}{T}$

These two equations can be combined to give the equation:

$\large&space;a=\frac{v^{2}}{r}$

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:

$\large&space;F=\frac{mv^{2}}{r}$

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 $\large&space;F=\frac{mv^{2}}{r}$ 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.