Second Moment of An Area of Geometric Shape

The second moment of an area of a geometric shape can be determined by integration or the parallel-axis theorem. Imply

Moment of Inertia of Areas

Second Moment of Area of Semi-circle

Second Moment about x by Double Integration

The second moment of an area of a semicircle about the axis x is

Second Moment about y' by Double  Integration

The second moment of an area of a rectangle about the centroidal axis y' is

Polar Moment about O from Rectangular Moments of Inertia

The polar moment of an area of a rectangle about the center O is

Second Moment of Area of Quarter-circle

Second Moment about x by Double Integration

The second moment of an area of a semicircle about the axis x is

Second Moment about y' by Double  Integration

The second moment of an area of a rectangle about the centroidal axis y' is

Polar Moment about O from Rectangular Moments of Inertia

The polar moment of an area of a rectangle about the center O is

Second Moment of Area of Ellipse

Second Moment about x'  by Double Integration

The second moment of an area of a ellipse about the centroidal axis x' is

Second Moment about y'  by Double Integration

Polar Moment about C from Rectangular Moments of Inertia

The polar moment of an area of a circle about the centroid C is