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If we are considering the semi circular wire of mass m to have a relatively small cross sectional radius, r compared to radius of the semi circular arc, R
And that we are considering the semi circular wire to lie in a xy plane. The mass moment of inertia taken about the z-axis (perpendicular to the plane) located at the cg position will be.
Izz=m*(R^2)*(PI-(4/PI))/PI
I did a check of this calculation with the way Catia calculated the same property. And the difference was found to be 0.03% When using the following geometry.
density=0.000001kgmm^3
Semi circular wire Radius R =60mm
cross sectional radius of wire = 1mm
results from Catia
V=592.176mm^3
m=0.000592176kg
Izz=1.268159kgmm^2
hand calculated results
V=592.176mm^3
m=0.000592176kg
Izz=1.267835kgmm^2
% difference [((1.268159)-(1.267835))/(1.267835)]*100=0.03%
Please carry out a check on the Izz calc. I determined it from 1st principles, so I may of made a mistake
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∙ 11y ago
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