A uniform helicopter rotor blade is 7.45 m long, has a mass of 126 kg, and is at

Question

A uniform helicopter rotor blade is 7.45 m long, has a mass of 126 kg, and is attached to the rotor axle by a single bolt. (a) What is the magnitude of the force on the bolt from the axle when the rotor is turning at 318 rev/min? (Hint: For this calculation the blade can be considered to be a point mass at its center of mass. Why?) (b) Calculate the torque that must be applied to the rotor to bring it to full speed from rest in 6.74 s. Ignore air resistance. (The blade cannot be considered to be a point mass for this calculation. Why not? Assume the mass distribution of a uniform thin rod.) (c) How much work does the torque do on the blade for the blade to reach a speed of 318 rev/min?

Explanation / Answer

a) Radius (r) of the helicopter rotor blade = 7.45m Mass (m) of helicopter rotor blade = 126kg Angular speed (?) of helicopter rotor blades =318rev/min = (318)(2p / 60)rad/s =33.30 rad/s Now formula for the magnitude of the force on the bolt fromthe axle when the rotor is turning at 318 rev/min is F = mr?2 Do the calculation work. b) We know that angular acceleration (a) of blade is a = ? / t = (33.30 rad/s) / (6.74s) Now formula for the torque is t = Ia = (mr2)a c) We know the formula for the amount workdone is W = (1/2)I?2 = (1/2)(mr2)?2 Do all the calculation work. Hope this helps you. Good luck with your homework and don't forget to rate.

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