Area Moment of Inertia - Filled Circular Sector

Description

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.
The second moment of area for a shape is easier to be calculated with respect to a parallel axis or with respect to a perpendicular axis through the centroid of the shape.
The formula calculates the Moment of Inertia of a filled circular sector or a sector of a disc of angle θ and radius r with respect to an axis going through the centroid of the sector and the center of the circle. The formula is valid for 0 ≤ θ ≤ π

Related formulas

Variables

IArea Moment of Inertia (mm4)
θAngle of circular sector (rad)
rRadius of circle (mm)