'On the Computation of the Moments of a Polygon, with some Applications'.

We have a comprehensive article explaining the approach to solving the moment of inertia. The second moment of area for a shape is easier to be calculeted with respect to a. The second moment of area is typically denoted with either an I : Cite journal requires |journal= ( help) The moment of inertia can be derived as getting the moment of inertia of the parts and applying the transfer formula: I I 0 + Ad 2. The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. A mistake that crops up in the calculation of moments of inertia, involves the Parallel Axis Theorem. The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The interactive calculates the moment of inertia of a semi-circle about three different axes using the parallel axis theorem. The diagram shows an arbitrary shape, and two parallel axes: the x axis, drawn in red, passes through the centroid of the shape at C, and the x axis, which is parallel and separated by a distance, d. The calculated result will have the same units as your input.

Enter the radius R or the diameter D below. For a list of equations for second moments of area of standard shapes, see List of second moments of area. Derivation We will use the defining equation for the moment of inertia (10.1.3) to derive the parallel axis theorem. This tool calculates the moment of inertia I (second moment of area) of a circle.

Moment of inertia circle derivation