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March 27, 2015

March 27, 2015

Posted by **Claire** on Wednesday, April 7, 2010 at 9:55am.

I am not working with mass. I am calculating moments of inertia Ix and Iy, and products of inertia using equations like ∫ y^2 dA and ∫ xy dA

- moments of inertia -
**drwls**, Wednesday, April 7, 2010 at 10:33amThe area moment of inertia can be verified with a beam deflection experiment. Load the beam at the middle with freely supported edges, or cantilevered from one wall with a clamped edge, for example.

For the polar moment of inertia about a perpendicular axis through the centroid, consider a torsional vibration experiment.

http://en.wikipedia.org/wiki/Polar_moment_of_inertia

Products of inertia will be harder to verify. It plays a role in the stability of motion and gyroscope behavior.

- moments of inertia -
**Damon**, Wednesday, April 7, 2010 at 11:10amIf you have a product of inertia, the axis you chose is not a principal axis of the figure.

If it were a body with mass, you could spin it about your chosen axis and see if it wobbles like a wheel with "dynamic imbalance". I am not sure how to do it with a zero mass figure on paper.

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