# Floating beads in parabolic wires

A bead of mass $m$ slides freely along a frictionless wire in the shape of the curve $y = x^{2}$ rotates around the $y$-axis with a constant angular velocity $\omega$. There is a constant downward gravitational acceleration $g$.

Suppose the bead maintains a constant height above the ground so that it "floats." How many such heights are possible?

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