Q1: (50 point) The blade of an oscillating fan and the rotor of its motor shown have a total weight of 1 kg and a combined radius of gyration (for all axes) of 100 mm. They are supported by bearings at A and B, 125 mm apart, and rotate at the rate $\omega_1 = 2000$ rpm.
Determine;
a) the dynamic reactions at A and B when the motor casing has an angular velocity $\omega_2 = (0.5 j + 1.5 k)$ rad/s.
b) the static reactions at A and B when the fan has stopped.
Note: Assume that the center of mass of the entire system is between the middle of the bearings of A and B, that is 62.5 mm away from bearing A.