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 0.150 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) Number___ Unit___

(b) Number___ Unit___

Answer 1

here,

angular accelration , alpha = 0.15 rad/s^2

theta = 2870 rev * 2pi

theta = 18023.6 rad

final angualar speed , w = 127 rad/s

a)

let the initial angular velocity of turbine be w0

using third equation of motion

w^2 - w0^2 = 2 * alpha * theta

127^2 - w0^2 = 2 * 18023.6 * 0.15

solving for w0

w0 = 103.5 rad/s

the initial angular speed is 103.5 rad/s

b)

let the time taken be t

using first equation of motion

w = w0 + alpha * t

127 = 103.5 + 0.15 * t

solving for t

t = 156.4 s