Question

The rotor of a turbojet engine of an aircraft has a mass $180kg$ and polar moment of inertia $10kg{m}^2$ about the rotor axis. The rotor rotates at a constant speed of $1100\text{rad/s}$ in the clockwise direction when viewed from the front of the aircraft. The aircraft while flying at a speed of $800\text{km per hour}$ takes a turn with a radius of $1.5$ to the left. The gyroscopic moment exerted by the rotor on the aircraft structure and the direction of motion of the nose when the aircraft turns are

• A. 162.9 N.m, the nose goes up
• B. 1629.6 N.m, the nose goes down
• C. 1629.6 N.m, and the nose goes up
• D. 162.9 N.m, and the nose goes down

Answer 1

The correct option is B 1629.6 N.m, the nose goes down

Given data:

$m=180kg$

$I=10kg-m^2$

$\omega =1100\text{rad/s}$

$R=1.5m$
$=1500m$

$v=800km/hr=800\times \frac{5}{18}$

$=222.222m/s$

${\omega }_p=\frac{v}{R}=0.14814\text{rad/s}$

Gyroscopic couple:

$=I.\omega .{\omega }_p\times 10\times 1100\times 0.14814$

$=1629.629N-m$

Active gyroscopic couple direction clockwise in a vertical plane looking from the left side of the aircraft.