A thin horizontal uniform \( \operatorname{rod} A B \) of mass \( m \) and length \( l \) can ro...

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A thin horizontal uniform \( \operatorname{rod} A B \) of mass \( m \) and length \( l \) can rotate freely about a vertical axis passing through its end A. At a certain moment the end B starts experiencing a constant force \( F \) which is always perpendicular to the original position of the stationary rod and directed in the horizontal plane. Find the angular velocity of the rod as a function of its rotation angle \( \varphi \) counted relative to the initial position.
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