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Area Moment of Inertia of an Annulus about a Centroidal Axis

The second moment of area, also known as moment of inertia of plane area, area moment of inertia or second area moment, is a geometrical property of an area that reflects how its points are distributed with regard to an arbitrary axis.

The second moment of area for an annulus equals the difference between the fourth powers of the inner and outer radius multiplied by \[Pi] divided by four.

Formula

QuantityVariable["J", "SecondMomentOfArea"] == (Pi*(QuantityVariable[Subscript["R", "1"], "Radius"]^4 - QuantityVariable[Subscript["R", "2"], "Radius"]^4))/4

symbol description physical quantity
J second moment of area "SecondMomentOfArea"
R1 outer radius "Radius"
R2 inner radius "Radius"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Area Moment of Inertia of an Annulus about a \ Centroidal Axis"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Area Moment of Inertia of an Annulus about a Centroidal Axis"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Area Moment of Inertia of an Annulus about a Centroidal Axis"], \ {QuantityVariable["J","SecondMomentOfArea"] -> Quantity[0.0460194`, ("Meters")^4]}]
Out[3]=

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