A pail of water is rotated in a vertical circle of

radius r = 1.49 m.
The acceleration of gravity is 9.8 m/s
2. What is the minimum speed of the pail at
the top of the circle if no water is to spill out?
Answer in units of m/s

2 answers

mg=mv²/r

v=sqrt(rg)
F=ma
(In rotation problems, centripetal acceleration is equal to V^2/r, where v is the velocity and r is the radius)
F=mv^2/r
The only force acting on the water bucket is that of gravity (mg).
mg=mv^2/r
Now we solve for v.
g=v^2/r
gr=v^2
√gr=v

√(9.8)(1.49)=v
14.6 m/s = v

This is the minimum speed because if it goes any slower it can't overcome the force of gravity (mg) and it will fall out.