Wind energy is gaining increased attention, so there is in turn an increased int

Question

Wind energy is gaining increased attention, so there is in turn an increased interest in windmill technology. Since the windmill blades (vanes) rotate about a central axis, one of the most important physical properties of a windmill is its moment of inertia. On the right is a picture of a typical windmill, where the geometry and center of mass of one of the vanes is illustrated. If the moment of inertia about axis A is 241 kg m2 and about axis B is 5860 kg m2, calculate the moment of inertia about the axis of rotation for the entire rotating assembly. The mass of each vane is 105 kg. (Ignore the hub and assume the vanes are flat.) A strong wind blows such that the windmill begins to rotationally accelerate. What happens to the moment of inertia during this increase in angular speed? The moment of inertia increases. The moment of inertia decreases. The moment of inertia does not change.

Explanation / Answer

Moment of Inertia about an axis perpendicular to both A and B at the poin of their intersection is I(1) = 547+13300 = 13847 kg m^2
Now this is the shifted moment of inertia, of one blade shifted from center of mass by 3.15m. But we need the moment of inertia for a shifted distance of 4.88m

I(1) = I(cm) + m(3.15)^2, but we need I(2) = I(cm) + m(4.88)^2. Solving the two equations we get

I(2) = I(1) + m ( 4.88^2 - 3.15^2) = 19556.57 kg m^2

This is moment of inertia due to one blade. For four blades it will be I(axis) = 4*I(2) = 78226.2836 kg m^2

Moment of inertia does not change, theoretically, considering that the shape of the blades dont bend due to shear stress of air.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.