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 0.111 rad/s2. After making 2870 revolutions, its angular speed is 131 rad/s. (a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up?

Question
Asked Oct 24, 2019
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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 0.111 rad/s2. After making 2870 revolutions, its angular speed is 131 rad/s. (a) What is the initial angular velocity of the turbine? (b) How much time elapses while the turbine is speeding up?

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Expert Answer

Step 1

Consider the initial angular speed of the turbine be ω0, the final angular speed of the turbine be ω, the angular acceleration of the turbine be α, the time elapses while the turbine speeds up be t, and the angular displacement of the turbine be θ.

 

The given values are,

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w=131 rad/s a 0.111 rad/s 2л гad Ө— 2л гad (2870 rev) = 18032.74 rad 1 rev 1 rev

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Step 2

(a)

 

Write the equation of angular motion, and solve for the...

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= Vo -2a0 (131 rad/s-2(0.111 rad/s(18032.74 rad) 114.7 rad/s

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Science

Physics

Angular Motion