# Acceleration of the tips of wind turbine blades

**1. The problem statement, all variables and given/known data**

A wind turbine has a rotor (its rotating section) which has a moment of inertia [itex]I = 1.26 × 10^7 \text{kgm}^2[/itex]. At peak output, with the rotor completing [itex]0.25 \text{ revolutions per second}[/itex], the turbine produces a power of [itex]P = 3\text{MW}[/itex]. The tips of the rotor blades sweep out a circle of diameter [itex]90 \text{m}[/itex].

Calculate the magnitudes of

(i) the acceleration of the tips of the blades,

(ii) the torque acting on the rotor shaft due to the wind,

(iii) the amount of rotational kinetic energy stored in the rotor,

(iv) the rotors angular acceleration should the wind suddenly cease to blow. [Ignore any torque on the blades due to air resistance.]

(v) Draw a sketch to show the direction of the acceleration of the blade tips.

**2. Relevant equations**

[itex]a=\omega^2r[/itex]

**3. The attempt at a solution**

The equation given above in obviously the centripetal acceleration, but this is not helpful for part ii. In fact, since I can only assume the rotor is travelling at constant [itex]\omega[/itex], surely the torque in part ii is 0. I’m just lost on this entire question.

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