Problem 6.8 Modem wind turbines are larger than they appear, and despite their a

Question

Problem 6.8 Modem wind turbines are larger than they appear, and despite their apparently lazy motion, the speed of the blades tips can be quite high-many times higher than the wind speed. A turbine has blades 55 m long that spin at 12 rpm (Figure 1) Part A At the tip of a blade, what is the speed? Express your answer to two significant figures and include the appropriate units. Part B At the tip of a blade, what is the centripetal acceleration? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

rpm to radians per second.
1 rev = 2 pi() radians
1 minute = 60 s
so 12 turns per minute = 12 * 2pi radians per minute = 12 * 2pi/ 60 radians per second.

Now v = wr = (12 * 2 * pi / 60) * 55 = 69.08 m/s

a = w^2 r
= (12 * 2 * pi / 60 ) ^ 2 * 55 = 86.76 m/s^2

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