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https://texercises.com/exercise/helicopter-rotor/
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Exercise:
A helicopter rotor blade can be considered a long thin rod. Each of the three rotor helicopter blades is lO long and has a mass of mO. How much torque must the motor apply to bring the blades up to a speed of wzO in tO?

Solution:
The moment of inertia of a long thin rod around an axis located at one of its s is according to Steiners parallel axis theorem: SolQtyJe/*mX*lX^kilogrammetersquared I_ fracmell^+mleftfracellright^ fracmell^ frac m qtyl^ Je This is the moment of inertia of one rotor blade. There are three therefore the total moment of inertia is: SolQtyJ*JeXkilogrammetersquared I J_ fracmell^ mell^ Je J To get a speed of wzO an angular acceleration of SolQtyalpwzX/tXradpsq alpha fracomegat fracpi ft fracwzt alp is necessary. The torque to be applied is: SolQtyMJX*alpXNm M Ialpha mell^ fracpi ft J alp M M fracpi f m ell^t M
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\(\LaTeX\)-Code
Exercise:
A helicopter rotor blade can be considered a long thin rod. Each of the three rotor helicopter blades is lO long and has a mass of mO. How much torque must the motor apply to bring the blades up to a speed of wzO in tO?

Solution:
The moment of inertia of a long thin rod around an axis located at one of its s is according to Steiners parallel axis theorem: SolQtyJe/*mX*lX^kilogrammetersquared I_ fracmell^+mleftfracellright^ fracmell^ frac m qtyl^ Je This is the moment of inertia of one rotor blade. There are three therefore the total moment of inertia is: SolQtyJ*JeXkilogrammetersquared I J_ fracmell^ mell^ Je J To get a speed of wzO an angular acceleration of SolQtyalpwzX/tXradpsq alpha fracomegat fracpi ft fracwzt alp is necessary. The torque to be applied is: SolQtyMJX*alpXNm M Ialpha mell^ fracpi ft J alp M M fracpi f m ell^t M
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Attributes & Decorations
Tags
acceleration, angular, inertia, mechanics, moment, of, physics, rotation, torque
Content image
Difficulty
(3, default)
Points
5 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
Decoration
File
Link