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