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\includegraphics[max width=\textwidth, alt={}, center]{de53978b-aa96-4fa2-a928-81a16450154e-3_468_550_1201_824} A wheel consists of a uniform circular disc, with centre \(O\), mass 0.08 kg and radius 0.35 m , with a particle \(P\) of mass 0.24 kg attached to a point on the circumference. The wheel is rotating without resistance in a vertical plane about a fixed horizontal axis through \(O\) (see diagram).

1. Find the moment of inertia of the wheel about the axis.
2. Find the distance of the centre of mass of the wheel from the axis. At an instant when \(O P\) is horizontal and the angular speed of the wheel is \(5 \mathrm { rad } \mathrm { s } ^ { - 1 }\), find
3. the angular acceleration of the wheel,
4. the magnitude of the force acting on the wheel at \(O\).