Centripetal Acceleration and Centripetal Force

We ended the previous lesson with a puzzle: an object in uniform circular motion moves at constant speed yet is accelerating. The resolution lies in recognizing that acceleration is the rate of change of velocity, and velocity is a vector. Even if the magnitude of the velocity stays fixed, a change in its direction is still a change in velocity, and therefore an acceleration must be present. This acceleration is called centripetal acceleration, from the Latin for "center-seeking," because it always points toward the center of the circle.

To see why the acceleration points inward, consider the velocity vectors at two nearby instants. Both are tangent to the circle, but slightly rotated relative to each other. The change in velocity, $\Delta\vec{v} = \vec{v}_2 - \vec{v}_1$, points roughly to