GATE ME 2019 Set 1 — Question 41
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Theory of Machines & Vibrations → Balancing, Flywheels & Gyroscopes → Gyroscope & Gyroscopic Couple
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Question
The rotor of a turbojet engine of an aircraft has a mass 180 kg and polar moment of inertia 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
Correct answer
(B) 1629.6 N·m and the nose goes down
Solution
1.Calculate Angular Velocity of Rotor ():
. Since it is clockwise viewed from the front, the spin vector points towards the rear of the aircraft.2.Calculate Angular Velocity of Precession ():
Velocity .Radius .
.
For a left turn, the precession vector points upwards.
3.Calculate Gyroscopic Moment ():
.4.Determine Direction of Nose Motion:
Using the right-hand rule:- Spin vector is backward ( direction).
- Precession vector is upward ( direction).
- Active gyroscopic couple (towards the left).
- Reactive gyroscopic couple (towards the right).
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