Problem: A racing car has a mass of 1000 kg. Each wheel has a mass of 20 kg and a radius of gyration of 0.3 m. The engine rotating parts have a mass of 15 kg and a radius of gyration of 0.1 m. The engine speed is 4 times the wheel speed. If the car takes a turn of 50 m radius at a speed of 108 km/h, calculate the gyroscopic couple.
Solution:
Calculate Moment of Inertia ($I$):
Calculate Angular Velocity ($\omega$ and $\omega_p$):
Calculate Total Angular Momentum:
(Referencing the standard formula derivation in Khurmi)
Total Gyroscopic Couple ($C$): $$ C = \omega_p \left[ 4 I_w \omega_w + I_e (G \times \omega_w) \right] $$
This is a simplified representative calculation.
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