The 8-lb rotor with radius of gyration of 3 in. rotates on ball bearings at a speed of 3000 rev/min about its shaft OG. The shaft is free to pivot about the X-axis, as well as to rotate about the Z-axis. Calculate the vector Ω for precession about the Z-axis. Neglect the mass of shaft OG and compute the gyroscopic couple M exerted by the shaft on the rotor at G.

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Vertical K 9" X, x 70°