An object's linear velocity remains unchanged when it is performing uniform circular motion because the change in velocity occurs in the form of a change in direction rather than speed. This is due to the presence of centripetal acceleration, which constantly acts toward the center of the circular path.
In uniform circular motion, the object moves along a circular path at a constant speed. Since velocity is a vector quantity that includes both speed and direction, any change in velocity means either a change in speed, direction, or both.
In the case of uniform circular motion, the object's speed remains constant because there is no change in its distance traveled per unit of time. However, the direction of the object's velocity constantly changes because it is always directed toward the center of the circle. This change in direction results in a continuous acceleration known as centripetal acceleration.
According to Newton's second law of motion, an object accelerates when a net force acts upon it. In uniform circular motion, the centripetal force provides the necessary acceleration to keep the object moving in a circular path. This centripetal force is always directed inward, perpendicular to the object's velocity vector at any point along the circle.
By maintaining a constant speed and changing only the direction of the object's velocity, the object's linear velocity (magnitude and direction) remains unchanged throughout the motion. It is important to note that although the linear velocity remains constant, the object is experiencing acceleration due to the centripetal force required to maintain the circular motion.