A typical propeller of a turbine used to generate electricity from the wind cons

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-34 m and a mass of m 405 kg. The propeller rotates at the rate of 23 rev/min. 120 (a) Convert the angular speed of the propeller to units of rad/s. rad/s (b) Find the moment of inertia of the propeller about the axis of rotation. (Treat each blade as a long, thin rod rotating about an axis perpendicular to its length and passing through its end.) (c) Find the total kinetic energy of the propeller.

Explanation / Answer

a)

w = 23 rev/min = 23 (2pi/60) rad/s = 2.41 rad/s

b)

m = mass of each blade = 405 kg

L = length of each blade = 34 m

Ib = moment of inertia of each blade = mL2/3 = (405)(34)2/3 = 156060 kgm2

Ip = moment of inertia of propeller = 3 x moment of inertia of each blade = 3 Ib = 3 x 156060 = 4.7 x 105 kgm2

c)

Total kinetic energy is given as

TKE = (0.5) Ip w2 = (0.5) (4.7 x 105) (2.41)2 = 1.4 x 106 J

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