Moment of Inertia

Question

How do we compute the moment of inertia matrix of a thin square plate of mass M with sides of size a?

Answer 1

The center of gravity (centroid) is at the "Mass Moment of Inertia" (center point of mass). If the object has more weight in 1 spot than the other the center is at another location.

If an object is placed to balance and the "moment" is not at the point used; that's the way it'll fall as a result of gravity. Earth's gp is 32.2ft/sec^2 or 9.81m.

Ix=Σ(y^2+z^2)dm

Iy=Σ(x^2+z^2)dm

Iz=Σ(x^2+y^2)dm