A toy helicopter consists of a rotor A with diameter d = 10 in. and weight Wr = 0.09 × 10−...

A toy helicopter consists of a rotor A with diameter d = 10 in. and weight Wr = 0.09 × 10−3 oz, a thin body B of length ℓ = 12 in. and weight WB = 0.144 × 10−3 oz, and a small ballast C placed at the front end of the body and with weight WC = 0.0723 × 10−3 oz. The ballast’s weight is such that the axis of the rotation of the rotor goes through G, which is the center of mass of the body B and ballast C. While holding the body (and ballast) fixed, the rotor is spun as shown with ω0 = 150 rpm. Neglecting aerodynamic effects, the weights of the rotor’s shaft and the body’s tail, and assuming there is friction between the helicopter’s body and the rotor’s shaft, determine the angular velocity of the body once the toy is released and the angular velocity of the rotor decreases to 120 rpm. Model the body as a uniform thin rod and the ballast as a particle. Assume that the rotor and the body remain horizontal after release.

Figure P8.73