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Moment of Inertia of a Thin Disk

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 disk of infinitesimal thickness, the moments of inertia are taken to be about the axes passing through the disk's center of mass.

The parallel moment of inertia is half the mass times the radius squared. The perpendicular moment of inertia is a quarter of the mass times the radius squared.

Formula

{QuantityVariable[Subscript["I", "∥"], "MomentOfInertia"] == (QuantityVariable["m", "Mass"]*QuantityVariable["r", "Radius"]^2)/2, QuantityVariable[Subscript["I", "⊥"], "MomentOfInertia"] == (QuantityVariable["m", "Mass"]*QuantityVariable["r", "Radius"]^2)/4}

symbol description physical quantity
I∥ parallel moment of inertia "MomentOfInertia"
m mass "Mass"
r radius "Radius"
I⊥ perpendicular moment of inertia "MomentOfInertia"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Moment of Inertia of a Thin Disk"]
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Get the formula:

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

In[3]:=
FormulaData[ ResourceObject[ "Moment of Inertia of a Thin Disk"], {QuantityVariable[ "m","Mass"] -> Quantity[1, "Kilograms"], QuantityVariable[ \!\(\*SubscriptBox[\("I"\), \("\[UpTee]"\)]\),"MomentOfInertia"] -> Quantity[0.3333333333333333`, "Kilograms" ("Meters")^2]}]
Out[3]=

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