GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 64 of 65

Marks: +1, -0

The rotor of a turbojet engine of an aircraft has a mass

180 {kg}

and polar moment of intertia 10

{kg} . {m}^{2}

about the rotor axis. The rotor rotates at a constant speed of

1100 {rad} \/ {s}

in the clockwise direction when viewed from the front of the aircraft. The aircraft while flying at a speed of 800

{km}

per hour takes a turn with a radius of

1.5 {km}

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

$162.9 {N} . {m}$ and the nose goes down
$1629.6 {N} . {m}$ and the nose goes up
$1629.6 {N} . {m}$ and the nose goes down
$162.9 {N} . {m}$ and the nose goes up

Validate

Solution:

m=180 {kg} ; I=10 {kg}- {m}^{2}

ω=1100

rad/s

ω_{p}=\;{V}/{R}=\;{800 × 5 {/} 18}/{1.5 × 1000}=0.148

rad/s
Gyroscopic couple

=I ω ω_{p}=10 × 1100 × 0.148=1629.6

N.m

When rotor rotates in the clockwise direction when viewed from the front of the aircraft, the noes goes down

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