2 A flywheel takes the form of a uniform disc of mass 8 kg and radius 0.15 m . It rotates freely about an axis passing through its centre and perpendicular to the disc. A couple of constant moment is applied to the flywheel. The flywheel turns through an angle of 75 radians while its angular speed increases from \(10 \mathrm { rad } \mathrm { s } ^ { - 1 }\) to \(25 \mathrm { rad } \mathrm { s } ^ { - 1 }\).

1. Find the moment of the couple about the axis. When the flywheel is rotating with angular speed \(25 \mathrm { rad } \mathrm { s } ^ { - 1 }\), it locks together with a second flywheel which is mounted on the same axis and is at rest. Immediately afterwards, both flywheels rotate together with the same angular speed \(9 \mathrm { rad } \mathrm { s } ^ { - 1 }\).
2. Find the moment of inertia of the second flywheel about the axis.