A helicopter rotor blade can be considered a long thin rod, as shown in figure b

Question

A helicopter rotor blade can be considered a long thin rod, as shown in figure below. If each of the three rotor helicopter blades is L = 3.89 m long and has a mass of m = 157 kg.

(a) calculate the moment of inertia of the three rotor blades about the axis of rotation.

(b) How much torque must the motor apply to bring the blades up to a speed of 5.13 revolutions per second in 8.53 s?

A helicopter rotor blade can be considered a long thin rod, as shown in figure below. If each of the three rotor helicopter blades is L = 3.89 m long and has a mass of m = 157 kg. calculate the moment of inertia of the three rotor blades about the axis of rotation. How much torque must the motor apply to bring the blades up to a speed of 5.13 revolutions per second in 8.53 s?

Explanation / Answer

(a) Moment Of Inertia about one end of a long thin rod is given by = (ML^2)/3 = [157 * (3.89)^2] / 3 = 791.91
but since there are three such rotor blades therefore
moment of inertia = 3 (791.91) = 2375.73

b) w (angular velocity) = 5.13 rev/s

We want that the rotor blades should stop in 8.53 seconds, therefore we need to find out the angular retardation to be brought about by the motor~

w2 (final angular velocity)= w1 (initial angular velocity) + at
0 = 5.13 + a(8.53)
a = - 5.13/8.53
a = - 0.6014

Torque = I a
Torque = 2375.73 x - 0.6014
Torque = - 1428.78

Ans. torque = - 1428.78

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