The turbine on a ship has a mass of 400 kg and is mounted on bearings A

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The turbine on a ship has a mass of 400 kg and is mounted on bearings A and B as shown. Its center of mass is at G, its radius of gyration is kz = 0.3 m, and kx = ky = 0.5 m. If it is spinning at 200 rad/s, determine the vertical reactions at the bearings when the ship undergoes each of the following motions: 

(a) Rolling, w₁ = 0.2 rad/s, 

(b) Turning, w₂ = 0.8 rad/s,

(c) Pitching, w3 = 1.4 rad/s.

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