Question

water is not to spill, what is the minimum velocity the pail can have? (b) How much time per revolution is this equivalent to? 

Answer 1

The minimum velocity $v$ is defined by the conditions required for the water not to spill. This is equivalent to the following value of time per revolution:

$$t=\frac 1n=\frac{2\pi}\omega=\frac{2\pi r}{v}.$$