Problem 1.245

A thin horizontal uniform 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 a horizontal plane. Find the angular velocity of the rod as a function of its rotation angle $\varphi$ counted relative to the initial position.