Suppose a rigid object is rotating around the \(z\) axis with angular velocity \(\omega_{1z}\) at time \(t_1\) and with angular velocity \(\omega_{2z}\) at a later time \(t_2\) (Figure 8-15). The \(\textbf{average angular acceleration}\) \(\alpha_{\mathrm{average},z}\) (the Greek letter \(\alpha\), or alpha) for the time interval between \(t_1\) and \(t_2\) is the change in angular velocity, \(\Delta{\omega_z} = \omega_{2z} - \omega_{1z}\) divided by the duration of the time interval, \(\Delta{t} = t_2 - t_1\):