Calculating Torque for Helicopter Blade Rotation

[9giddjl]

Homework Statement

Consider a simple helicopter blade, attached to a bolt at its end. The bolt is made to rotate by a powerful motor, and the blade therefore rotates. The blade has a length L= 7.8 m and mass M= 100 kg. The blade is shaped approximately like a long thin, uniform rod.
What torque must the bolt exert on the blade in order to bring it from rest to full angular speed 320 rev/min in time t= 6.70 s

Homework Equations

Before, I worked out the force that ther bolt exerts on the blade when the blade is spinning at full speed to be 4.4 x 10^5 N. thus, force= 4.4 x 10^5 N. I thought that i could just find the angular acceleration: wf=wi + at and then find the moment of inertia and use T=Ia but i don't know what the moment of inertia would be. Would it be 1/12mL^2 or 1/3mL^2

The Attempt at a Solution

I found the angular acceleration to be 5/rad/s^2.. but i just don't know what the moment of inertia would be becoz i worked them out using the above equations and i keep getting the wrong answer. the right answer is 7.6 x 10^3 N.m. Is T=Ia the right formula to be using or am i on the wrong track? Any help would be muchly appreciated! thankyou!

 

[tiny-tim]

… use T=Ia but i don't know what the moment of inertia would be. Would it be 1/12mL^2 or 1/3mL^2

Hi 9giddjl!

(try using the X² tag just above the Reply box )

It's 1/12 mL² about the centre of a rod,

and using the parallel axis theorem it's 1/12 mL² + 1/4 mL² = 1/3 mL² about the end

 

[9giddjl]

i used 1/2 ML^2 for the moment of inertia and it yielded the correct answer! thankyou for ur help wise teacher!:)