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Angular velocity, often denoted by the Greek letter omega (ω), is a vector quantity that measures the rate of change of an object's angular position with respect to time. It is defined as the change in angle per unit time, and its SI unit is radians per second (rad/s). Angular velocity is a crucial concept in rotational kinematics and dynamics, describing how quickly an object is rotating around a fixed axis.

In a circular motion, the angular velocity is related to the linear velocity (v) and the radius (r) of the circular path by the equation v = ωr. This relationship highlights the connection between the rotational and translational motion of an object.

Angular velocity can be either constant or variable, depending on the nature of the rotation. In uniform circular motion, the angular velocity is constant, while in non-uniform circular motion, it varies with time. The time derivative of angular velocity gives the angular acceleration, which describes how the rate of rotation changes over time.

In three-dimensional space, angular velocity is represented as a pseudovector, with its magnitude and direction indicating the speed and axis of rotation, respectively. The right-hand rule is often used to determine the direction of the angular velocity vector.

Angular velocity plays a significant role in various fields, including physics, engineering, and astronomy. It is used to analyze the motion of rotating objects, design machinery, and study celestial bodies' rotational dynamics. Understanding angular velocity is essential for comprehending the principles of rotational motion and applying them to real-world problems.