The rotor of the turbine of a ship has a mass of 2500 kg and rotates at a speed of 3200 rpm counter-clockwise when viewed from stern. The rotor has radius of gyration of 0.4 m. Determine the gyroscopic couple and its effect when:
(i) the ship steers to the left in a curve of 80 m radius at a speed of 15 knots (1 knot = 1860m/h)
(ii) the ship pitches 5 degrees above and 5 degrees below the normal position and the bow is descending with its maximum velocity - the pitching motion is simple harmonic with a periodic time of 40 seconds.
(iii) the ship rolls and at that instant, its angular velocity is 0.4 rad/s clockwise when viewed from stern. Also find maximum angular acceleration during pitching.