Question

A wind turbine is rotating counterclockwise at 0.6 rev/s and slows to a stop in 12 s. Its blades are 23 m in length. (a) What is the angular acceleration of the turbine? (b) What is the centripetal acceleration of the tip of the blades at t = 0 s? (c) What is the magnitude and direction of the total linear acceleration of the tip of the blades at t = 0 s?

Answer 1

(a) Given the frequency of rotation (number of rotations per second) f = 0.6rev/s, So the initila angular velocity

It slows to stop in t = 12s. So the final angular velocity = 0. So we can write,

So the angular acceleration of the wind turbine is 0.42rad/s2.

(b) Given the length of the blades is l = 23m. The centripetal acceleration is given by,

So the centripetal acceleration of the tip of the blade at t = 0s is 581.12m/s2.

(c) The tangential acceleration of the tip of the blade at t = 0s is,

So the magnitude of total linear acceleration is given by,

The magnitude of total linear acceleration is 581.20m/s2.

Its direction is given by,

So the direction of total linear acceleration at t=0s is from the tangential acceleration vector.