Question

Derivation of area moment of inertia of rectangle

Answer 1

Consider a rectangle with base and height whose centroid is located at the origin. represents the second moment of area with respect to the x-axis; represents the second moment of area with respect to the y-axis; represents the polar moment of inertia with respect to the z-axis.

Answer 2

Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass, the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr2. That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.