GATE 2021 ME (ME1) – Question 34
The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is 100 kg.m². The propeller rotates at $\omega=12$ rad/s. The waves acting on the ship hull induces a rolling motion as shown in the figure with an angular velocity of 5 rad/s. The gyroscopic moment generated on the shaft due to the motion described is _____ N.m (round off to the nearest integer).
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Correct answer: 0
Explanation
Gyroscopic torque is the vector product $\boldsymbol\Omega\times\mathbf H$, with H=Iω along the shaft. Rolling rotates the ship about this same longitudinal axis.
The vectors are parallel, so their cross product is zero. **Answer: 0 Nm**. Multiplying IωΩ alone would incorrectly assume perpendicular precession.