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{composition-setup}{composition-setup}

{excerpt}The rate of change of the [angular velocity] with time, or the second derivative of the [angular position] with respect to time.  For systems rotating about a single [axis|axis of rotation] with a fixed [moment of inertia] about that axis, the angular acceleration is directly proportional to the net [torque|torque (single-axis)] acting on the [system].{excerpt}  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}