What is the direction of the change in velocity (∆v) between two infinitesimally close points on a circular path?

On a circular path, the velocity of an object is constantly changing direction, even if the speed remains constant. This constant change in direction is a result of the circular motion, which is influenced by a centripetal force pulling the object toward the center of the circle.

When analyzing the change in velocity (∆v) between two infinitesimally close points on that circular path, it's important to recognize that velocity is a vector quantity, which means it has both magnitude and direction. As the object moves along the circular path, while the speed may not change, the direction of its velocity does change.

Since the change in velocity reflects the difference in the velocity vectors at the two points, it will always point towards the center of the circular path. This is fundamental to understanding circular motion, as any object moving in a circle experiences a net inward force directed toward the center, which is responsible for the continuous change in direction of the velocity vector. Thus, the direction of the change in velocity is characterized as being toward the center of the circle, illustrating how circular motion is maintained through centripetal acceleration.