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| angular acceleration average angular acceleration instantaneous angular acceleration | — — — | кутове прискорення середнє кутове прискорення миттєве кутове прискорення |
Angular acceleration characterizes the rate of change of angular velocity, while linear acceleration characterizes the rate of change of linear velocity. There is average acceleration and instantaneousacceleration.
If the angular velocity 
of a rotating body is not constant, the body has an angular acceleration. Let and 
be the angular velocities at times t2 and t1, respectively. The average angular acceleration of the rotating body in the interval from t2 to t1, is defined as
where 
is the change in the angular velocity that occurs during the time interval ∆ t.
The (instantaneous) angular acceleration 
, is the limit of this quantity as ∆ t is made to approach zero. Thus
Instantaneous angular acceleration equals the first derivative of angular velocity
with respect to time or the second derivative of the angular displacementwith respect to time
Unit of measurement of angular acceleration is the radiant per second-squared (rad/s2) or the revolution per second-squared (rev/s2).
Angular acceleration is an axial vector too. If the angular velocity increases along time, vectors of the angular acceleration and the angular velocity have the same direction. If the angular velocity decreases along time, vectors of the angular acceleration and the angular velocity have the opposite direction.
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| Active vocabulary | | | In order to calculate angular acceleration it is enough to know the equation of rotational motion |