Question

A typical propeller of a turbine used to generate electricity from the wind consists of three blades as in the figure below. Each blade has a length of L = 33 m and a mass of m = 415 kg. The propeller rotates at the rate of 21 rev/min. 120degree angle between blades
a) Convert the angular speed of the propeller to units of rad/s.
(b) Find the moment of inertia of the propeller about the axis of rotation.___J · s2
(c) Find the total kinetic energy of the propeller.______ J

Answer 1

This is pretty standard question. What is it you do not understand?

For the moment of inertial figure each blade rotating about its end, then multiply by three.

KE=1/2 Itotal*w^2

Answer 2

(A) w = (21rev/min) * (1min/60sec) * (2pi rad/1rev) = 2.2 rad/s

(B)

I = MR^2
I = (415kg)(33m)^2
I = 4.52E5 (I for one propeller)

I for all three propellers = (4.52E5) * 3 = 1.36E6

(C) KE = (1/2) * Iw^2

= (1/2)(4.52E5)(2.2)^2
=1.1E6 J

The book gives solutions for I and KE using one propeller. My thought were to multiply I *3....a little confusing. Thoughts...?