(Not a homework question as the answer is below.)
"A bucket full of water is swung in a loop with a radius r. What is the frequency you need to swing it at (revolutions per second) to keep the water from falling out?"
The answer turns out to involve three formulas:
gravitational acceleration = centripetal acceleration
a = ω²r
f = ω/2π
But none of these are really apparent at first sight (to me).
Is there any kind of systematic process or is the answer supposed to just jump out at you?
If you are good at these kinds of problems, what process is your mind going through?