Okay, can someone help me out with this physics problem:
You have a marble moving in a hemispherical (frictionless) "bowl". The vertical distance from the marble to the bottom of the bowl is y, and the radius of the hemisphere is R. What is the minimum angular velocity, in terms of R, y, and g (acceleration of gravity), at which the marble will continue to move in a circle (rather than sliding down to the bottom of the bowl)?
For context, this is the second part of a three-part problem. The first part asked for an expression for the angular velocity, and I got sqrt(g/(R-y)), which was correct.
I want to set the y-component of the Normal force greater than or equal to mg, because that would make the net acceleration vector point downward (and toward the center of the circle). But whenever I do that, I just end up with the same thing that I got for the first part (sqrt(g/(R-y))), which is wrong.