as always in these sorts of problems you start by sketching a force diagram. There are two forces acting on the bucket. What are they?
A bucket of mass 2kg is attached to a rope of length 2 meters and is swinging in a vertical circle. The speed of the bucket at the lowest point is 10m/s.
a) find the tension in the rope as a function of the angle.
b) show that the tension in the rope reaches a maximum value when the bucket is at the lowest point.
am not sure what equation to start of with? Any help appreciated.
Without gravity, the centripetal force is F= ma where "a" is the acceleration toward the center of the circle. You can calculate that knowing the speed of the pail. Once you have found that force, add it to the force of gravity.
This equation comes from an equality of angular momentum in terms of the moment of inertia and the angular momentum for a point particle. It is not likely to solve your problem as the question has nothing to do with this.
You seem to be looking for someone to give you the final answer. You've been around enough to know we don't simply do that. If nothing else your equation doesn't use the tension anywhere so that should tell you something. Go back and take a look at the other posts and see if you can follow the logic to get to the solution.
-Dan
centripetal force is what you're after. It always points inwards towards the center of rotation and the opposite reaction, plus gravity, is what creates tension on the rope.
the magnitude of the force is $\dfrac {m|v|^2} r$
draw the force body diagram now that you know about this force.
You might try drawing it w/o gravity to begin with, as if you were spinning a bucket deep in space.