Wind energy is gaining increased attention, so there is in turn an increased int
ID: 2244974 • Letter: W
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.
The picture is 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 547 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. The picture is 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 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
Ip = IA + IB (according to perpendicular axis theorem)
IP = 547 + 13300
IP = 13847 kg.m^2
now according to parallel axis theorem
IP = Icm + M*d1^2
Icm = Ip - M*d^2
Icm = 13847 105*(3.15)^2
Icm = 12805 kg.m^2
Io = Icm + M*d2^2 (abot rotating axis)
Io = 12805 + 105*4.88^2
Io = 15305 kg.m^2
I_total = 4*Io = 61222 kg.m^2
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