I think I understand it now...
For the bucket, F(c)=F(g)+T, which, as Hootenanny said, can be written as F(g)+T=m*v^2/r. At the minimum speed, however, the rope will be "loose", meaning that there is no tension. Thus, T=0 and mg=m*v^2/r, g=v^2/r
For the water inside the bucket...