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# angular velocity (rotational velocity)

Angular velocity, also called rotational velocity, is a quantitative expression of the amount of rotation that a spinning object undergoes per unit time. It is a vector quantity, consisting of an angular speed component and either of two defined directions or senses.

The magnitude, or length, of the angular velocity vector is directly proportional to the angular speed, and is measured in the same units as angular speed (radians per second, degrees per second, revolutions per second, or revolutions per minute). The direction of the angular velocity vector is perpendicular to the plane in which the rotation takes place. If the rotation appears clockwise with respect to an observer, then the angular velocity vector points away from the observer. If the rotation appears counterclockwise, then the angular velocity vector points toward the observer.

Consider a car rolling forward along a highway. The angular velocity vectors for all four tires point toward the left along the lines containing the wheel axles. If the car speeds up, the vectors get longer. If the car slows down, the vectors get shorter. If the car stops, the vector lengths become zero. If the car is put into reverse, the vectors reverse their directions, and point toward the right along the lines containing the wheel axles.

Compare angular speed. Also see speed, velocity, radian per second, and degree per second.

This was last updated in September 2005

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