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 . After making 2870 revolutions, its angular speed is 133 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. the initial angular velocity = 166.5rad/s

b. t= 135.7seconds

Explanation:

a. v = rw

angular velocity for 2870 rev, w = (2πN)/60 =2*3.142*2870rev)/60 =300.5rad/sec

w₁-w₂ = 300.5 - 133= 166.5rad/s

the initial angular velocity = 166.5rad/s

acceleration = change in velocity / time

b. 1 revolution = 2π

1 rad = 0.159rev

? = 2870 rev

=2870*1)/0.159 = 18050.3rad

the final angular speed = rev/time = rad/time

133 rad/s = 18050.3/t

133t = 18050.3

t= 135.7seconds