Problem

A rotor, spinning freely about the fixed point O, consists of a thin uniform bar AB that f...

A rotor, spinning freely about the fixed point O, consists of a thin uniform bar AB that functions as a hub and two identical blades pinned at A and B, respectively. The dimensions of the system are: d = 0.5 m, ℓ = 5 m, and w = 0.3 m. The bar AB has a mass mAB = 30kg, and each of the blades has a mass mb = 20 kg. Each blade can be modeled as a uniform thin plate. The angular speed is ωr = 100 rpm when the angle θ is equal to 90°. At some point, an internal mechanism causes the blades to change orientation relative to AB in such a way that θ becomes constant and equal to 180°. Neglecting aerodynamic forces and friction at the bearings at O, determine the angular speed of the rotor after θ = 180°.