Modern wind turbines are larger than they appear, and despite their apparently l

Question

Modern 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 58 m long that spin at 12 rpm .
Part A At the tip of a blade, what is the speed?

Part B At the tip of a blade, what is the centripetal acceleration?
Modern 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 58 m long that spin at 12 rpm .
Part A At the tip of a blade, what is the speed?

Part B At the tip of a blade, what is the centripetal acceleration?

Part A At the tip of a blade, what is the speed?
Part A At the tip of a blade, what is the speed?

Part B At the tip of a blade, what is the centripetal acceleration?

Explanation / Answer

length= r = 58 m

angular velocity = w = 12 rpm = 12 x 2 pie/ 60 = 1.256 rad / sec

a) speed = v = r w = 58 * 1.256 = 72.85 m/sec

b) ac = r w^2 = 58 * 1.256^2 = 91.5 m/sec^2

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