Nonuniform Circular Motion-Newtonian bucket problem

[Dougggggg]

Homework Statement

Word for word from textbook. . .
"You tie a cord to a pail of water, and you swing the pail in a vertical circle of a radius of 0.600 m. What minimum speed must you give the pail at the highest point of the circle if no water is to spill from it?"

R=0.600 m
g=9.80 m/s²

Homework Equations

I tried to use this though I am unsure if it can be used since I believe this is a case of nonuniform circular motion.
a_rad = $$\frac{v^2}{R}$$ = $$\frac{4\pi^2 R}{T^2}$$

I have also tried using $$\Sigma$$F equations but those lead me into a mess.

The Attempt at a Solution

I first tried to figure out what forces were involved at the top and bottom of the circle. I kept getting things that I couldn't really do anything with since I only knew one acceleration. I then went on to look at what I could do with a_rad and kept making a mess of algebra that wasn't really helping anything at all. I know how this problem works conceptually to some degree, the inertia makes the water resistant to change directions and so on, but I am not getting how I am supposed to do the math here. If someone could give me some idea of which direction I should start going I would be greatly appreciative.Edit: Found right answer, if I ignored tension as a force acting on the bucket then I came up with a_rad = g
then
$$\sqrt{gR}$$ = v

Solved for v. I am not sure how that gives me the minimum speed required to complete the circle but it said it was the right answer in the back of the book. If anyone could please explain why that math worked the way it did I would be really really really thankful.

Answer was v = 2.43 m/s

Edit 2: Does it work because for that whole equation to work v has to be big enough to complete a whole circle?

 

[rock.freak667]

The usual centripetal motion way would require a tension or a normal reaction to give the speed 'v'.

It is easier this time to just use conservation of energy. If you consider a line through the center of the circle as your 0 energy line, at the highest point, the height is the radius 'R'.
It has associated PE 'mgR'.

At the highest point the bucket with water is moving at a speed 'v' and the associated KE is 0.5mv².

You however just can't ignore the tension,as that would mean at the highest point, there is not tension at all, meaning that the cord would go slack and the bucket would fall to the ground shortly after reaching the highest point.

 

[Dougggggg]

The usual centripetal motion way would require a tension or a normal reaction to give the speed 'v'.

It is easier this time to just use conservation of energy. If you consider a line through the center of the circle as your 0 energy line, at the highest point, the height is the radius 'R'.
It has associated PE 'mgR'.

At the highest point the bucket with water is moving at a speed 'v' and the associated KE is 0.5mv².

You however just can't ignore the tension,as that would mean at the highest point, there is not tension at all, meaning that the cord would go slack and the bucket would fall to the ground shortly after reaching the highest point.

We haven't discussed circular motion to that extent yet. It probably can be noted as a force on the ex, it may just be tangent to the top of the circle. Therefore, with gravity, would cause an acceleration ahead of the normal. Which makes sense because it has the most acceleration at the top of the circle.