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

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.)

Explanation / Answer

Ip = IA + IB (according to perpendicular axis theorem)

IP = 241 + 5860

IP = 6101 kg.m^2


now according to parallel axis theorem

IP = Icm + M*d1^2

Icm = Ip - M*d^2

Icm = 6101 105*(2.85)^2

Icm = 5248.14 kg.m^2


Io = Icm + M*d2^2 (abot rotating axis)

Io = 5248.14 + 105*4.42^2

Io = 7300 kg.m^2


I_total = 4*Io = 29200 kg.m^2

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