Please help me! Wind energy is gaining in increased attention, so there is in tu

Question

Please help me!

Wind energy is gaining in 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 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 547 kg m2 and about axis B is 13300 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.)

Explanation / Answer

Moment of inertia about an axis passing through the intersection to A and B axis and parallel to axis of rotation:

I(about c)= I(about A)+ I(about B)=547+13300=13847 kg.sq. m

net mass of the system,M= 4*mass of each vane= 4* 105= 420 kg.

so, Moment of inertia about the C.G. of the whole system i.e. at centre and about the axis of rotation,

by parallel axis theorem:

I(about c.g.)= I(about c) + Mass of system *(distance betwn both axes)^2

= 13847 + 420 (5.35)^2

= 25868.45 kg. m^2

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