A uniform thin rod of length \(L\) and mass \(M\) is pivoted at one end and allowed to swing in a vertical plane. Let \(\theta\) be the angle the rod makes with the downward vertical direction, as shown in the figure. The rod is released from rest at some initial angle \(\theta_0 > 90^\circ\). What is the ratio \(\dfrac{\alpha_{45}}{\alpha_{90}}\) of the magnitude of the angular acceleration of the rod when it is at \(\theta = 45^\circ\) to the magnitude of its angular acceleration when it is at \(\theta = 90^\circ\)?