Centripetal Acceleration

Acceleration is any change in velocity, and velocity is a vector with both size and direction. An object moving in a circle at constant speed never changes how fast it goes, but it constantly changes which way it's pointing. That changing direction is a changing velocity, so by definition the object is accelerating, every single instant, even though a speedometer on it would never move.

You can see where this acceleration points by comparing two velocity arrows taken an instant apart along the circle. Both arrows have the same length, since speed is constant, but they point in slightly different directions. If you draw them tail to tail and find the arrow connecting their tips, that difference vector points inward, toward the center of the circle. As the time between the two snapshots shrinks toward zero, that inward direction becomes exact: the acceleration at any instant points directly at the center, perpendicular to the velocity at that moment. This is why it's called centripetal, meaning center-seeking. The size of this acceleration is a = v² / r, where v is speed and r is the radius of the circular path.

This idea connects directly to the next step in circular motion, where that inward acceleration gets tied to an inward net force through F = ma. Nothing about centripetal acceleration explains what causes it physically; tension, friction, gravity, or a normal force can all supply it. The acceleration itself is purely a geometric consequence of moving in a curve, which is why it shows up before any discussion of what force produces it.