What Is the Minimum Speed to Prevent Water Spillage in a Rotating Pail?

[lunarskull]

nonuniform circular motion

a pail of water is rotated in a vertical circle of radius 1m. what is the minimum speed of the pail at the top of the circle if no water is to spill out?

hmmm this problem is difficult for me to do because they gave only 1 variable. i drew a freebody diagram (i doubt if i did it right) and came up with the equation t+mg=m(v^2/r) am i doing this right?

 

[Doc Al]

Right, assuming that "t" is the force exerted by the pail on the water. As long as the pail exerts some non-zero force, the water remains in the pail; when that force goes to zero, the water begins to spill out.