# Around And Around

A particle $$P$$ is attached to a fixed point $$O$$, which is $$0.8 \, \text{m}$$ above a smooth horizontal plane, by a light inextensible string of length $$1.0 \, \text{m}$$.

The particle moves in a circle with angular speed $$\omega \, \text{rad s}^{-1}$$. Given that $$P$$ stays in contact with the plane, find the maximum value of $$\omega ^2$$.

Note: Let $$g = 9.8 \text{m s}^{-2}$$.

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