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Moment of Inertia of a Triangular Plate

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

The moment of inertia of a uniform triangular plate about the vertical axis passing through its center of mass is proportional to the sum of the squares of the sides and the mass.

Formula

QuantityVariable[Subscript["I", "z"], "MomentOfInertia"] == ((QuantityVariable["a", "Length"]^2 + QuantityVariable["b", "Length"]^2 + QuantityVariable["c", "Length"]^2)*QuantityVariable["m", "Mass"])/36

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Moment of Inertia of a Triangular Plate"]
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Get the formula:

In[2]:=
FormulaData[ResourceObject["Moment of Inertia of a Triangular Plate"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Moment of Inertia of a Triangular Plate"], {QuantityVariable[ \!\(\*SubscriptBox[\("I"\), \("z"\)]\),"MomentOfInertia"] -> Quantity[2, "Kilograms" ("Meters")^2], QuantityVariable["b","Length"] -> Quantity[1.2`, "Meters"], QuantityVariable["m","Mass"] -> Quantity[1, "Kilograms"], QuantityVariable["c","Length"] -> Quantity[1.2`, "Meters"]}]
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