What Are the Two Values of b for Steady Precession in a Gyroscope?

[mattyboson12]

[Question]
Homework Statement [/b]
A special purpose fan is mounted as shown in figure Q5 (Ive attached a picture of the diagram). The motor, armature, shaft and blades have a combined mass of 2.2Kg with a radius of gyration of 60mm. The axial position of b of the 0.8kg block A can be slid on the mounting shaft. With the fan turned off, the unit is balanced about the x-axis when b=180mm

The motor and fan operate at 1725rev/min (180.6 rad/s) in the direction shown. Determine the two values of b that will produce a steady procession of 0.2rad/s about the y-axis.

[Attempt]
I have drawn a free body diagram of unit rotating due to gyroscopic forces (Attached). I worked out the moment of inertia was (60*10^-3)^2*2.2= (7.92*10^-3) kgm^2. I then worked out that the gyroscopic force generated by the fan was (7.92*10^-3)*(0.2)*(180.6)=0.286Nm. I am really confused how to work out the distance that the weight moves either towards or away from the pivot to cause this torque.

 

[paisiello2]

Try summing the moments about R.