If the vertical tail propeller of a helicopter is absent, the helicopter will ro

Question

If the vertical tail propeller of a helicopter is absent, the helicopter will rotate about its yaw axis every time the angular speed of its main blades is changed. Assuming that each of the helicopter's four main blades are L = 6 m long with a mass of 30 kg, estimate the final angular momentum of the helicopter cabin if it is initially at rest, the vertical tail propeller is broken, and the angular speed of the main blades is increased from 200 rpm to 400 rpm. The mass moment of inertia with respect to the mass center of the helicopter cabin is 250 kg-m^2 and the mass center is on the same axis as the center of the main rotor's blades. Neglect air drag on the main blades. a) omega = 1002 rpm b) omega = 1102 rpm c) omega =1122 rpm d) omega = 1152 rpm

Explanation / Answer

here ,

L = 6 m

m = 30 Kg

inital angular speed , wi = 200 rpm

final angular speed , wf = 400 rpm

wf = 400 s

I = 250 Kg.m^2

let the final angular speed is w

Using conservation of angular speed

4 * 1/3 * 30 * 6^2 * (400 - 200) = 250 * w

solving for w

w = 1152 rpm

the final angular speed is d) w = 1152 rad/s

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