Problem 1.281

A horizontally oriented uniform rod \(A B\) of mass \(m=\) \(=1.40 \mathrm{~kg}\) and length \(l_{0}=100 \mathrm{~cm}\) rotates freely about a stationary vertical axis \(O O^{\prime}\) passing through its end \(A\). The point \(A\) is located at the middle of the axis \(O O^{\prime}\) whose length is equal to \(l=55 \mathrm{~cm}\). At what angular velocity of the rod the horizontal component of the force acting on the lower end of the axis \(O O^{\prime}\) is equal to zero? What is in this case the horizontal component of the force acting on the upper end of the axis?