Centripetal Acceleration

Definition

The inward-pointing acceleration that keeps an object moving in a circle — constantly changing its direction, not its speed.

$a_c = \frac{v^2}{r}$

Symbol: $a_c$ · Unit: m/s²

Technical definition

For uniform circular motion, a_c = v²/r = ω²r, directed toward the center of the circle. It is the acceleration required by Newton's second law to produce the net inward (centripetal) force.

Example

A car taking a 50 m radius curve at 20 m/s needs 8 m/s² of centripetal acceleration — provided by friction between tires and road. Too fast, and friction cannot supply it.

Common confusion

There is no outward ‘centrifugal force’ in an inertial frame — that is just inertia. The real acceleration points inward. Centrifugal effects only appear as a pseudo-force in the rotating frame.