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.