3 A uniform rod, of mass 0.75 kg and length 1.6 m , rotates in a vertical plane about a fixed horizontal axis through one end. A frictional couple of constant moment opposes the motion. The rod is released from rest in a horizontal position and, when the rod is first vertical, its angular speed is $3 \mathrm { rad } \mathrm { s } ^ { - 1 }$.\\
(i) Find the magnitude of the frictional couple.\\
\includegraphics[max width=\textwidth, alt={}, center]{de53978b-aa96-4fa2-a928-81a16450154e-2_584_527_1798_822}

A disc is rotating about the same axis. The moment of inertia of the disc about the axis is $0.56 \mathrm {~kg} \mathrm {~m} ^ { 2 }$. When the rod is vertical, the disc has angular speed $4.2 \mathrm { rad } \mathrm { s } ^ { - 1 }$ in the opposite direction to that of the rod (see diagram). At this instant the rod hits a magnetic catch $C$ on the disc and becomes attached to the disc.\\
(ii) Find the angular speed of the rod and disc immediately after they have become attached.

\hfill \mbox{\textit{OCR M4 2003 Q3 [7]}}