The GATE Grind

GATE 2026 ME – Question 20

Theory of Machines · Gyroscope · 1 mark · Multiple choice

The rotor of an aeroplane engine has a mass moment of inertia 1.0 kg m$^2$. The engine rotates at a speed of 500 RPM in the clockwise direction if viewed from the front of the aeroplane. If the aeroplane while flying at 1200 km/hr turns with a radius of 2 km at same elevation, then the magnitude of the gyroscopic moment exerted by the rotor on the aeroplane structure in N m is

  1. 8.73
  2. 17.46
  3. 4.37
  4. 26.19

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Show answer and explanation

Correct answer: (A) 8.73

Explanation

The spin speed is $\omega = \frac{2\pi \times 500}{60} = 52.36$ rad/s. The aeroplane speed is $\frac{1200}{3.6} = 333.3$ m/s, so the precession rate is $\omega_p = \frac{333.3}{2000} = 0.1667$ rad/s. The gyroscopic moment is $I\omega\omega_p = 1.0 \times 52.36 \times 0.1667 = 8.73$ N m.