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Area (Polar) Moment of Inertia of a Cylinder

The formula and equation for the area moment of inertia of a hollow or solid cylinder, also known as the polar moment of inertia (second moment of area) of a solid or hollow cylinder, is below.  The formula is the same for movement about its axis or about its end or diameter:

 , where:

I = Area Moment of Inertia of Cylinder (m^4) (expressed as j or I)

ro = Outer Radius (m)

Area Moment of Inertia

 , where:

I = Area Moment of Inertia about the y-axis (m^4)

z = Distance from the y-axis (m)

A = Elemental Area (m^2)

Area Moment of Inertia of a Circle

 , where:

I = Area Moment of Inertia of Circle (m^4)

r = Radius (m)

Area Moment of Inertia of a Rectangle

 , where:

I = Area Moment of Inertia about x-axis (m^4)

b = Length about x-axis (m)

y = Length about y-axis (m)

Beam Shear (Jourawski Equation)

The Jourawsky Formula for shear stress (formula di jourawski), as derived from the shear stress formula, has many real world examples:

 , where:

 = Shear Stress (Pa)

V = Shear Force (N)

Q = First Moment of Area (m^3)

I = Area Moment of Inertia (m^4)

t = Thickness (m)

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