A uniform thin rod of length \(L\) and mass \(M\) is attached to a frictionless pivot at one end. The rod is released from rest in a horizontal position and allowed to rotate downward. Let \(\alpha_0\) be the magnitude of the angular acceleration of the rod at the instant of release. Let \(\alpha_{45}\) be the magnitude of the angular acceleration of the rod when it has rotated through an angle of \(45^\circ\) below the horizontal. What is the ratio \(\dfrac{\alpha_{45}}{\alpha_0}\)?