Question

The turbine rotor of a ship has a mass of 2200 kg and rotates at 1800 rpm clockwise when viewed from the aft (rear end). The radius of gyration of the rotor is 320 mm The gyroscopic couple if the ship turns right at a radius of 250 m with a speed of 25 km/h is

• A. 1400 N-m
• B. 1180 N-m
• C. 1000 N-m
• D. 1500 N-m

Answer 1

The correct option is B 1180 N-m

$m=2200\text{kg,}R=250\text{m,}$
$N=1800\text{rpm,}k=0.32\text{m}$

$v=25\text{km/h}=\frac{25\times 1000}{3600}=6.94\text{m/s}$

$I={\text{mK}}^2=2200\times (0.32{)}^2=225.3{\text{kg.m}}^2$

$\omega =\frac{2\pi \times 1800}{60}=188.5\text{rad/s}$

${\omega }_p=\frac{v}{R}=\frac{6.94}{250}=0.0278\text{rad/s}$

$C=I\omega {\omega }_p$

$=225.3\times 188.5\times 0.0278=1180\text{N-m}$