Hi this is my question, Wind energy is gaining increased attention, so there is

Question

Hi this is my 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 middot m2 and about axis B is 5860 kg middot m2, calculate the assembly. The mass of each vane is 411 kg. (Ignore the hub and assume the vanes are flat.) Number kg middot m2 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

Ic is the moment of inertia abt centre and I is moment of inertia abt Centroid

Ib = I +mr^2

Ic = I+m*R^2

Ic = Ib-mr^2+m*R^2

Ic = 5860 - 411*2.75^2 +411*4.26^2 = 10210.5 Kg.m^2

Moment abt rotating axis = Ic+Ia = 10210.5 +241 = 10451.5

since four vanes are there

Total MI = 4*10451.5 = 41806 Kgm^2

Remains const

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