5 Four identical uniform rods, each of mass \(m\) and length \(2 a\), are rigidly joined to form a square frame \(A B C D\). Show that the moment of inertia of the frame about an axis through \(A\) perpendicular to the plane of the frame is \(\frac { 40 } { 3 } m a ^ { 2 }\). The frame is suspended from \(A\) and is able to rotate freely under gravity in a vertical plane, about a horizontal axis through \(A\). When the frame is at rest with \(C\) vertically below \(A\), it is given an angular velocity \(\sqrt { } \left( \frac { 6 g } { 5 a } \right)\). Find the angular velocity of the frame when \(A C\) makes an angle \(\theta\) with the downward vertical through \(A\). When \(A C\) is horizontal, the speed of \(C\) is \(k \sqrt { } ( g a )\). Find the value of \(k\) correct to 3 significant figures.