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angular acceleration is the rate of change of the [angular velocity] with time, or the second derivative of the [angular position] with respect to time. It's the angular analogue to linear [acceleration]. Like the angular velocity, it is a vector quantity, having both direction and magnitude. It is usually represented by the small Greek letter alpha, *α*.
{latex}\begin{large} \[ \vec{\alpha} = \frac{d{\vec{\omega}}}{dt} = \frac{d^{2}{\vec{\theta}}}{dt^2} \] \end{large}{latex}