Centripetal Force

A common misconception is that "centripetal force" is a new type of force that exists alongside tension, friction, gravity, etc. In reality, centripetal force is simply the name we give to the net force pointing toward the center of a circular path. It describes the role a force plays, not a distinct force itself.

When an object moves in a circle, it experiences centripetal acceleration $a_c = \frac{v^2}{r}$ directed toward the center. By Newton's second law, this acceleration requires a net force:

This net force must point toward the center. The centripetal force is this net force—it's provided by real, physical forces like tension, friction, gravity, or normal forces.

Consider a ball whirling on a string. The string exerts tension $\vec{T}$ on the ball, pointing toward the center. If tension is the only force in the radial direction, then the net force is simply $\vec{T}$. We call this net force the centripetal force: $F_c = T$. We don't add an additional "centripetal force" to our free body diagram—that would double-count the same force.