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Moment of Inertia of an Elliptical Lamina

The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analog to mass. For a uniform elliptical lamina, the moments of inertia are taken to be about the vertical axis passing through the lamina's center of mass.

The moment of inertia is proportional to the sum of the squares of the semimajor and semiminor axes times the mass.

Formula

QuantityVariable[Subscript["I", "z"], "MomentOfInertia"] == ((QuantityVariable["a", "Length"]^2 + QuantityVariable["b", "Length"]^2)*QuantityVariable["m", "Mass"])/4

symbol description physical quantity
Iz moment of inertia "MomentOfInertia"
a semimajor axis "Length"
b semiminor axis "Length"
m mass "Mass"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Moment of Inertia of an Elliptical Lamina"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Moment of Inertia of an Elliptical Lamina"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Moment of Inertia of an Elliptical Lamina"], {QuantityVariable[ "m","Mass"] -> Quantity[1, "Kilograms"], QuantityVariable["b","Length"] -> Quantity[1.2`, "Meters"]}]
Out[3]=

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