Traagheidsmomenten: Probleemoplossing

Consider airplanes, where the wing components are triangular plates. Approximating this component as a schematic triangle, what is the moment of inertia about the centroidal axis?

The centroid of a triangle is located at one-third of the triangle's height from its base.

Consider a differential strip at a certain distance from the base parallel to the centroidal axis. This strip's differential moment of inertia equals the square of the distance from the axis times the differential area.

The differential area is the product of the strip's length and width. The strip's length is estimated considering the law of similar triangles.

Integrating the differential moment of inertia along the entire height gives the moment of inertia about the base.

Using parallel axis theorem, the moment of inertia about the centroid equals the moment of inertia about the base minus the product of the traingle's area and the square of the distance from the centroidal axis.

Substituting the values, the moment of inertia of the triangle about the centroidal axis is obtained.