Acceleration is present in uniform circular motion due to the constant change in the direction of velocity.

In physics, acceleration is defined as the rate of change of velocity over time. This change can occur in magnitude (speed), direction, or both. In uniform circular motion, while the object’s speed remains constant, the direction of its velocity continuously alters. This alteration in direction constitutes an acceleration.

To illustrate this concept, consider an object moving along a circular path at a constant speed. At any given point during its motion, the object’s velocity vector is tangent to the circular path, pointing in the direction of its instantaneous motion. As the object advances along the circle, this tangent direction changes, indicating that the velocity vector is also changing. Although the speed—which is the magnitude of the velocity vector—remains constant, the change in direction signifies that the velocity itself is not constant.

This change in velocity leads to an acceleration known as centripetal acceleration. This type of acceleration is always directed toward the center of the circular path. The term ‘centripetal’ is derived from the Latin words ‘centrum,’ meaning ‘center,’ and ‘petere,’ meaning ‘to seek,’ which aptly describes the orientation of this acceleration.

The magnitude of centripetal acceleration can be expressed with the formula:

where $v$ denotes the speed of the object and $r$ represents the radius of the circular path. This equation illustrates that the acceleration increases if the object’s speed increases or if the radius of the circle decreases.

In summary, despite the constant speed of an object in uniform circular motion, the ongoing change in the direction of its velocity results in an acceleration. This phenomenon explains why acceleration occurs in uniform circular motion.