Discussion
The rotor of an aeroplane engine has a mass moment of inertia 1.0 kg \(\text{m}^{2}\). 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
Answer: A
The gyroscopic moment is about 8.73 N m.
The spin speed is \(\omega = 2\pi(500)/60 = 52.36\) rad/s. The precession rate is the aeroplane's angular velocity in the turn, \(\omega_{p} = v/R\), with \(v = 1200/3.6 = 333.3\) m/s:
\[ \begin{aligned} \omega_{p} &= 333.3/2000 = 0.1667\ \text{rad/s} \\ C &= I\omega\omega_{p} = 1.0 \times 52.36 \times 0.1667 = 8.73\ \text{N m} \end{aligned} \]
17.46 and 26.19 are two and three times the value, and 4.37 half of it. The clockwise sense of rotation decides the direction of the moment (nose up or down), not its size.
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