# angular acceleration

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## angular acceleration

See angular velocity.## Angular Acceleration

a vector quantity that characterizes the rate of change of the angular velocity of a rigid body.

In the case of rotation about a fixed axis, the angular acceleration and angular velocity can be treated as scalars. If the angular velocity (angular speed) ω to increases or decreases uniformly, the angular acceleration is ∊ = Δω/Δ*t*, where Δω is the increase in ω occurring during the time interval Δ*t*. In the general case of rotation about a fixed axis, ∊ = *d*ω/*dt* = *d*^{2}φ/*dt*^{2}, where φ is the rotation angle of the body.

The angular acceleration vector e is aligned with the axis of rotation; this vector points in the direction of the angular velocity vector ω for accelerated rotation and in the opposite direction for decelerated rotation. In the case of rotation about a fixed point, the angular acceleration is defined as the first derivative of the angular velocity ω with respect to time—that is, ∊ = *dω/dt*—and is directed along the tangent to the hodograph of ω at the corresponding point. Angular acceleration has the dimension *T ^{–2}*, where

*T*is time.