Question

A wind turbine has a radius of 30 m, a moment of inertia of 9.0 ×...

A wind turbine has a radius of 30 m, a moment of inertia of 9.0 × 106kg⋅m2, and rotates with an initial angular speed of 2.0 rad/s. When the wind speed increases, the turbine experiences a net torque of 1.6× 105N⋅m. What is the linear speed of the tips of the turbine blades 27 s after the acceleration begins?

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Answer #1

The initial angular momentum of the turbine is

The angular impulse applied to the turbine is

The final angular momentum is therefore

.

So, the final angular speed of the turbine is

And the linear speed of the tip of the blade is therefore given by

So, the answer to this problem is 74.4 m/s.

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