Falling Rod

Its time to pick up the Fallen Rod

Determine the minimum coefficient of friction between a uniform rod and floor at which a person can slowly lift the rod without slippage to the vertical position, applying to its end a force perpendicular to it. Answer will be of the form \[\displaystyle{{ \mu }_{ min }=\cfrac { 1 } { a\sqrt { b } } }\]

Give \(a+b\).

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