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# angular acceleration (rotational acceleration)

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

The magnitude, or length, of the angular acceleration vector is directly proportional to the rate of change of angular velocity, and is measured in radian s per second squared (rad/s 2 or rad · s -2 ). Alternatively, the angular acceleration magnitude can be expressed in degrees per second squared (deg/s 2 or deg · s -2 ). The direction of the angular acceleration vector is perpendicular to the plane in which the rotation takes place. If the increase in angular velocity appears clockwise with respect to an observer, then the angular acceleration vector points away from the observer. If the increase in angular velocity appears counterclockwise, then the angular acceleration vector points toward the observer.

The angular acceleration vector does not necessarily point in the same direction as the angular velocity vector. Consider a car rolling forward along a highway at increasing speed. The angular acceleration vectors for all four tires point toward the left along the lines containing the wheel axles. If the car stops accelerating and maintains a constant velocity, the angular acceleration vectors disappear. If the car slows down going forward, the vectors reverse their directions, and point toward the right along the lines containing the wheel axles. If the car is put into reverse and increases velocity going backwards, the angular acceleration vectors point toward the right along the lines containing the axles. If the backward velocity is constant, the angular acceleration vectors vanish; if the backward velocity decreases, the angular acceleration vectors point toward the left along the lines containing the wheel axles.

This was last updated in January 2011

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