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Moment of Inertia of an Ellipsoid

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 solid ellipsoid, the moments of inertia are taken to be about the vertical axis passing through the ellipsoid's center of mass.

The moment of inertia of a uniform solid ellipsoid is proportional to the sum of the squares of the semiaxes of the ellipsoid and the mass.

Formula

QuantityVariable[Subscript["I", "z"], "MomentOfInertia"] == ((QuantityVariable["a", "Length"]^2 + QuantityVariable["b", "Length"]^2)*QuantityVariable["m", "Mass"])/5

symbol description physical quantity
Iz moment of inertia "MomentOfInertia"
a semiaxis in x direction "Length"
b semiaxis in y direction "Length"
m mass "Mass"

Forms

Examples

Get the resource:

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

Get the formula:

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

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Moment of Inertia of an Ellipsoid"], {QuantityVariable[ "b","Length"] -> Quantity[1.2`, "Meters"], QuantityVariable[ \!\(\*SubscriptBox[\("I"\), \("z"\)]\),"MomentOfInertia"] -> Quantity[2, "Kilograms" ("Meters")^2]}]
Out[3]=

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