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 radii of gyration are $k_z = 0.3$m, and $k_x = k_y = 0.5$m. If the turbine is spinning at 200 rad/s, determine the vertical reactions at the bearings when the ship undergoes each of the following motions:
(a) rolling, $\omega_1 = 0.2$ rad/s: Reaction forces $A_y = $ , $B_y = $ kN
(a) turning, $\omega_2 = 0.8$ rad/s: Reaction forces $A_y = $ , $B_y = $ kN
(a) pitching, $\omega_3 = 1.4$ rad/s: Reaction forces $A_y = $ , $B_y = $ kN
Provide all answers in kN using one decimal place.