A vertical pole is mounted on a frictionless horizontal floor. A small ring is fixed to the pole at a height $H$ above the floor. A small block of mass $m$ slides on the floor in a circle around the pole. It is connected to the ring by a massless spring with spring constant $k$ and relaxed length $L_0$. If the block is made to revolve around the pole with a constant angular velocity $\omega$, it will slide outward until the spring provides the necessary centripetal force for that radius. At a certain critical angular velocity $\omega_c$, the block just loses contact with the floor. What is $\omega_c$? Assume that the parameters are such that the block rests on the floor when $\omega=0$, and lifts off at a finite, non-zero radius.