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?

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