The top of a circular wire, with diameter 1.0 m, is firmly connected to a vertical steel rod. The wire passes through the hole in the center of a precious red ring, initially situated almost at the lowest point (point A ). As the rod spins up slowly about its vertical axis, the ring moves slowly upward along the wire, toward point B, as shown. Find the maximum angular speed, in rotations per second, at which the ring remains in the position where the angle ϕ = 45∘. Assume the coefficient of friction between the ring and the wire is 0.40.
