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 0.113 rad/s2. After making 2870 revolutions, its angular speed is 139 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

here, for the angle rotated ,

theta = 2870 rev = 2870 * 2pi rad

theta = 18029 rad

a = 0.113 rad/s^2

wf = 139 rad/s

a) let the initial angular velocity of the turbine is wi

Using third equation of motion

wf^2 - wi^2 = 2 *a * theta

139^2 - wi^2 = 2 * 0.113 * 18029

solving for wi

wi = 123.5 rad/s

the initial angular speed of the turbine is 123.5 rad/s

b)

time interval = (wf - wi)/a

time interval = (139 - 123.5)0.113

time interval = 137.4 s

the time interval is 137.4 s