A helicopter rotor is formed by attaching the ends of three 157kg blades, 4.23 m

Question

A helicopter rotor is formed by attaching the ends of three 157kg blades, 4.23 m in length and spaced at equal angles to one another, to a massless center hub. To maintain lift, the blade tips must remain subsonic (vsound=343 m/s). Determine the torque the helicopter motor must supply to bring this rotor to its maximum operational speed in 11.8 seconds. Ignore any frictional interactions.

My question: Can the inertia be calculated as a disk since the system of blades behaves like a solid mass?

My solution:

Explanation / Answer

v = r*w

==> w = v/r = 343/4.23 = 81.087 rad/s

alfa = dw/dt = 81.087/11.8 = 6.87 rad/s^2

I = 3*(m*L^2/3) = m*L^2 = 157*4.34^2 = 2809.18 kg.m^2

we know, T = I*alfa

= 2809.18*6.87

= 19299 N.m

we can treat it as disk.

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