One of the limitations on the design of modern windmills for the generation of e

Question

One of the limitations on the design of modern windmills for the generation of electricity is that the tip of the blades must not exceed the speed of sound in air (340 meters per second). Otherwise you would get the pressure of the sonic "boom" on the blades that would severely impede the motion of the blades, as well as produce the persistent noise of the boom that would severely impede the prospects of re-election of the politician who had the windmill installed. You come across such a windmill while driving through the mid-west and you estimate the length of its blades to be 42.0 meters. Being a closet physicist you take out your pocket watch and count the revolutions of the blades in one minute to be 46.0.
a) The blade tip speed is what fraction of the speed of sound?

b) What is the acceleration of the blade tips, in m/s2?

Explanation / Answer

Speed of tip = 2*pi*r*46 /60

= 202.32 m/s

Fraction of speed of sound = 202.32/340 = 0.595

(b) a = v^2/r = 202.32^2 /42 = 974.6 m/s^2

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