2. A uniform equilateral triangular lamina \(A B C\) has mass \(m\) and sides of length \(\sqrt { } 3 a\). The lamina is free to rotate in a vertical plane about a fixed smooth horizontal axis \(L\), which passes through \(A\) and is perpendicular to the lamina. The midpoint of \(B C\) is \(D\). The lamina is held with \(A D\) making an angle of \(60 ^ { \circ }\) with the upward vertical through \(A\) and released from rest. The moment of inertia of the lamina about the axis \(L\) is \(\frac { 5 m a ^ { 2 } } { 4 }\) Find the speed of \(D\) when \(A D\) is vertical.
(8)