Question

A wind turbine has 3 wings, each 50.0 m long from the central shaft to the wing tip. The turbine is rotated at 35 rev/minutes. a. What is the linear speed of the wing tip, in m/s? b. What is the radial acceleration of the wing tip expressed in units of the gravitational acceleration, g?

Answer 1

Solution :

Here we have given :

Length of the wing : L = 50 m

Angular speed : ω = 35 rev/min =  (35 x 2π rad) / (60 sec) = 3.665 rad/s

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Part (a) Solution :

The linear speed of the wing tip will be : v = ω L = (3.665 rad/s)(50 m) = 183.26 m/s

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Part (b) Solution :

And, Radial acceleration will be given by : a_r = v² / L = (183.26 m/s)² / (50 m) = 671.68 m/s²

Since, Acceleration due to gravity is : g = 9.81 m/s²

Thus : a_r = (671.68 m/s²) / (9.81 m/s²) = 68.5 g

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