I determined the area moment of inertia and the product of inertia of the cross-section of a beam about the centroidal axes using equations. I am now asked to design an experiment to verify the results that I obtained through equations. Can someone please suggest an experiment because I don't know how to continue?

Question

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

Answer 1

The 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.

Answer 2

If 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.