In the helicopter shown, a vertical tail propeller is used to prevent rotation o

Question

In the helicopter shown, a vertical tail propeller is used to prevent
rotation of the cab as the speed of the main blades is changed.
Assuming that the tail propeller is not operating, determine the
final angular velocity of the cab after the speed of the main blades
has been changed from 180 to 240 rpm. (The speed of the main
blades is measured relative to the cab, and the cab has a centroidal
moment of inertia of 650 lb ft s2 Each of the four main blades is
assumed to be a slender 14-ft rod weighting 55 lb.)

Answer is given in back of book: -24.4 RPM, but can't figure out how to get to the answer

In the helicopter shown, a vertical tail propeller is used to prevent rotation of the cab as the speed of the main blades is changed. Assuming that the tail propeller is not operating, determine the final angular velocity of the cab after the speed of the main blades has been changed from 180 to 240 rpm. (The speed of the main blades is measured relative to the cab, and the cab has a centroidal moment of inertia of 650 lb ft s2 Each of the four main blades is assumed to be a slender 14-ft rod weighting 55 lb.) Answer is given in back of book: -24.4 RPM, but can't figure out how to get to the answer

Explanation / Answer

Blades moment of inertia:
4 ml2/3 = 4 (55/32.17)(14)2/3 = 446.7
Ib 0b = Ib b + Ic c

Ib 0b = Ib (b + b/c) + Ic c

Ib ( b/c - 0b)= -(Ib + Ic ) c

c = - Ib /(Ib + Ic ) ( b/c - 0b)

c = - 446.7/(446.7 + 650) (240-180) = -24.4 rpm

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