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 0.155 rad/s2. After making 2870 revolutions, its angular speed is 127 rad/s. (a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up?

a) Initial angular velocity of the turbine = 102.66 rad/s

b) Time elapsed while the turbine is speeding up = 157 s

Explanation:

a) Considering angular motion of turbine:-

Initial angular velocity, u = ?

Acceleration, a = 0.155 rad/s²

Final angular velocity, v = 127 rad/s

Angular displacement, s = 2π x 2870 = 18032.74 rad

We have equation of motion v² = u² + 2as

Substituting

v² = u² + 2as

127² = u² + 2 x 0.155 x 18032.74

u = 102.66 rad/s

Initial angular velocity of the turbine = 102.66 rad/s

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

Initial angular velocity, u = 102.66 rad/s

Acceleration, a = 0.155 rad/s²

Final angular velocity, v = 127 rad/s

Substituting

v = u + at

127 = 102.66 + 0.155 x t = 157 s

Time elapsed while the turbine is speeding up = 157 s