Uniform circular motion refers to the motion of an object traveling along a circular path at a constant speed, while its direction continuously changes. In other words, the magnitude of the object's velocity remains constant, but its velocity vector constantly changes direction, resulting in circular motion. Despite the change in direction, the object's speed remains the same throughout the motion.

Key Characteristics of Uniform Circular Motion:

1. Constant Speed: The object travels at a constant speed along the circular path.

2. Change in Direction: The velocity vector of the object changes direction continuously, always pointing tangentially to the circle.

3. Acceleration: Even though the speed is constant, there is acceleration present due to the change in direction of velocity. This acceleration is called centripetal acceleration and is always directed toward the center of the circle.

4. Angular Velocity (ω): Angular velocity represents the rate of change of the angle through which an object rotates in a given time. It is related to linear speed (v) and radius (r) of the circular path by the equation v=rω.

5. Period (T): The time required for the object to complete one full revolution along the circular path is called the period of the motion.

6. Frequency (f): The number of revolutions the object completes in one unit of time is called the frequency of the motion.

Derivation of v=rω: