Twirling a bucket around...confused?

The rope goes slack if the tension in it is zero. The tension will be zero if gravity supplies the necessary acceleration for its circular motion, that is g = v^2/r or at the velocity sqrt(1.5m*9.8m/s^2) = 3.8m/s. At any velocity lower than this, you are likely to get wet if there is any water in the bucket . . .