Well...I am able to work the problem just fine on the x' and y' axes using the standard vector analysis of r X F, I just have no idea how to transfer it to the x and y axes. I provided a picture of the actual problem, alongside the actual answer in the solutions manual. I don't understand how they get the -sin30 for translating the moment about the x' axis to the y direction...and why that is even done. Shouldn't we just take the y' moment and cos30 it to get the moment about the y axis? Those are my thoughts...if anyone can clarify I'll wash their car.