A thin, non-uniform rod of total mass \(M\) and length \(L\) has a linear mass density given by \(\lambda(x) = \dfrac{2M}{L^2}x\), where \(x\) is the distance from the rod's lighter end. The rod is attached to a frictionless horizontal pivot at the end \(x = 0\) and held in a horizontal orientation. Immediately after the rod is released from rest, what is the magnitude of its angular acceleration about the pivot?