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```Second Moment of An Area of Geometric Shape  Moment of Inertia of Areas   Second Moment of Area of Semi-circle    Second Moment about x by Double Integration    Second Moment about y' by Double  Integration    Polar Moment about O from Rectangular Moments of Inertia    Second Moment of Area of Quarter-circle    Second Moment about x by Double Integration    Second Moment about y' by Double  Integration    Polar Moment about O from Rectangular Moments of Inertia    Second Moment of Area of Ellipse    Second Moment about x'  by Double Integration    Second Moment about y'  by Double Integration    Polar Moment about C from Rectangular Moments of Inertia ```

# 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

#### Polar Moment about C from Rectangular Moments of Inertia

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

ID: 121000008 Last Updated: 10/18/2012 Revision: 0 Ref:

References

1. I.C. Jong; B.G. rogers, 1991, Engineering Mechanics: Statics and Dynamics
2. F.P. Beer; E.R. Johnston,Jr.; E.R. Eisenberg, 2004, Vector Mechanics for Engineers: Statics

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