Solution to task 155 from Chertov´s for extramural stud

155. A man stands on Zhukovsky´s bench and holds a bicycle wheel in his hand by the axle, rotating around its axis with an angular velocity ω1 = 25 rad / s. The axis of the wheel is located vertically and coincides with the axis of the Zhukovsky bench. At what speed ω2 will the bench rotate if the wheel is turned around the horizontal axis at an angle α = 90 °? The moment of inertia of the person and the bench J is 2.5 kg m2, the moment of inertia of the wheel J0 = 0.5 kg m2.