Question

6.8 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 56 m long that spin at 14 rpm . At the tip of a blade, what is the speed? At the tip of a blade, what is the centripetal acceleration?

Answer 1

Formula for calculating the speed and centripetal acceleration of any objects moving in uniform circular motion are

Velocity = radius * angular velocity

v = r*w

Centripetal acceleration =  angular velocity ^2 * radius

a = w^2 * r

Now convert given rpm to angular velocity

Angular velocity= (2*pi*rpm)/60

w = 2*pi *14 /60 radians/second

Substitute in the above formulas to compute velocity and Centripetal acceleration

Velocity= 2*pi*14/60 * 56

= 82 m/s

Acceleration

a = w^2 * r

= (2*pi*14/60)^2 * 56

= 120 m/s^2