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Area Moment of Inertia of a Regular Pentagon 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 a regular pentagon equals edge length to the fourth power multiplied by a constant.

Formula

QuantityVariable["J", "SecondMomentOfArea"] == (Sqrt[265 + 118*Sqrt[5]]*QuantityVariable["a", "Length"]^4)/96

symbol description physical quantity
J second moment of area "SecondMomentOfArea"
a edge length "Length"

Forms

Examples

Get the resource:

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

Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Area Moment of Inertia of a Regular Pentagon about a Centroidal \ Axis"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Area Moment of Inertia of a Regular Pentagon about a Centroidal \ Axis"], {QuantityVariable["J","SecondMomentOfArea"] -> Quantity[0.239551`, ("Centimeters")^4]}]
Out[3]=

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