Couple applied to rotating body

1 A circular flywheel of radius 0.3 m , with moment of inertia about its axis \(18 \mathrm {~kg} \mathrm {~m} ^ { 2 }\), is rotating freely with angular speed \(6 \mathrm { rad } \mathrm { s } ^ { - 1 }\). A tangential force of constant magnitude 48 N is applied to the rim of the flywheel, in order to slow the flywheel down. Find the time taken for the angular speed of the flywheel to be reduced to \(2 \mathrm { rad } \mathrm { s } ^ { - 1 }\).

1 A wheel is rotating freely with angular speed \(25 \mathrm { rad } \mathrm { s } ^ { - 1 }\) about a fixed axis through its centre. The moment of inertia of the wheel about the axis is \(0.65 \mathrm {~kg} \mathrm {~m} ^ { 2 }\). A couple of constant moment is applied to the wheel, and in the next 5 seconds the wheel rotates through 180 radians.

1. Find the angular acceleration of the wheel.
2. Find the moment of the couple about the axis.

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.