State the necessary condition for the law of conservation of angular momentum to be applied to a system of rotating bodies.
An autonomous underwater vehicle utilizes a twin-rotor propulsion system where Rotor 1 and Rotor 2 rotate concentrically about the same longitudinal axis. Before an internal coupling is engaged, the states of the two rotors are as follows:
| Rotor | Moment of inertia / kg m2\text{kg m}^2kg m2 | Initial angular speed / rad s−1\text{rad s}^{-1}rad s−1 | Initial direction of rotation (viewed from the rear) |
|---|---|---|---|
| 1 | 4.0 | 90 | Clockwise |
| 2 | 8.0 | 30 | Anticlockwise |
An electromagnetic clutch is engaged, forcing the two rotors to couple. Frictional torque acts between them, causing slipping for a brief period until both rotors rotate together at a common angular speed. Calculate this common angular speed and state whether the final direction of rotation is clockwise or anticlockwise when viewed from the rear.
Two different model specifications for the electromagnetic clutch, designator P and designator Q, provide different constant frictional torques during the slipping phase:
| Clutch model | Frictional torque during slipping / N m\text{N m}N m |
|---|---|
| P | 400 |
| Q | 250 |
For reliable thermal dissipation, the slipping duration during engagement must be between 0.6 s0.6\text{ s}0.6 s and 1.1 s1.1\text{ s}1.1 s. Determine which clutch model(s), P or Q (or both), satisfy this operational constraint.
