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Parallel Axis Theorem

The parallel axis theorem can be used to determine the mass moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between the axes.

The parallel moment of inertia equals the mass times the axial distance squared plus the moment of inertia about the center of mass.

Formula

QuantityVariable[Subscript["I", "∥"], "MomentOfInertia"] == QuantityVariable["m", "Mass"]*QuantityVariable["r", "Length"]^2 + QuantityVariable[Subscript["I", "CM"], "MomentOfInertia"]

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Parallel Axis Theorem"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Parallel Axis Theorem"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Parallel Axis Theorem"], {QuantityVariable["r","Length"] -> Quantity[1, "Meters"], QuantityVariable["m","Mass"] -> Quantity[1, "Kilograms"]}]
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