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Moment of Inertia of a Cylinder

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

The parallel moment of inertia is half the mass times the square of the radius. The perpendicular moment of inertia is proportional to the mass times the sum of the height squared and three 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["h", "Height"]^2 + 3*QuantityVariable["r", "Radius"]^2))/12}

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

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Moment of Inertia of a Cylinder"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Moment of Inertia of a Cylinder"]]
Out[2]=

Use some values:

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

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