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angular accelerationSee angular velocity.
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/Δt, where Δω is the increase in ω occurring during the time interval Δt. In the general case of rotation about a fixed axis, ∊ = dω/dt = d2φ/dt2, 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.