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 0.100 rad/s2. After making 2844 revolutions, its angular speed is 140 rad/s.

Complete answer

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 0.100rad/s2. After making 2844 revolutions, its angular speed is 140rad/s

(a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up?

a) 126.59 radians per second

b) 134.1 seconds

Explanation:

We can use the rotational kinematic equations for constant angular acceleration.

a) For a) let’s use:

(1)

with the initial angular velocity, the final angular velocity, the angular acceleration and the revolutions on radians (2844 revolutions = 17869.38 radians). Solving (1) for initial velocity:

b) Knowing those values, we can use now the kinematic equation

with t the time, solving for t: