Question

A wind turbine is initially spinning at a constant angular speed. As the wind’s strength gradually increases, the turbine experiences a constant angular acceleration of 0.140 rad/s2. After making 2870 revolu- tions, its angular speed is 137 rad/s. (a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up?

Answer 1

Answer:

a)   Initial angular speed = 117.13 rad/s

b)  Time elapsed = 141.92 s

Explanation:

a) We have equation of motion v² = u² + 2as

   Final angular speed, v = 137 rad/s

   Angular acceleration, a = 0.140 rad/s²

   Displacement,s = 2870 x 2π = 18032.74 rad

Substituting

   v² = u² + 2as

   137² = u² + 2 x 0.140 x 18032.74

    u² = 13719.83

    u = 117.13 rad/s

 Initial angular speed = 117.13 rad/s

b) We have equation of motion, v = u +at

            137 = 117.13 + 0.140  t

             t = 141.92 s

 Time elapsed = 141.92 s