Statics

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Polar Moment of Inertia of a Hollow Cylinder

The polar moment of inertia of a hollow cylinder (j), where the inner diameter and outer diameter are known, also known as the formula for the second moment of area of a hollow cylinder, is derived from the second moment of area and results in:

Polar moment of hollow cylinder, where:

J = Polar Moment of Inertia of a hollow cylinder (m^4)

 = pi, 3.1415...

Polar Moment of Inertia of a Rectangle

The polar moment of inertia of a rectangle or rectangular cross section (j), also known as the formula for the second moment of area of a rectangle, is derived from the second moment of area and results in:

, where:

J = Polar Moment of Inertia of a rectangle or rectangular section (m^4)

Polar Moment of Inertia of a Square

The polar moment of inertia of a square or square cross section (j), also known as the formula for the second moment of area of a square, is derived from the second moment of area and results in:

 , where:

J = Polar Moment of Inertia of a square or square section (m^4)

b = Length or width of the square's sides (m)

Porosity

 , where:

 = Porosity

VV = Volume of Void Space

VT = Total Volume of Material (Including Void)

Potential Energy of a Spring

 , where:

E = Potential Energy of a Spring (J)

k = Spring Constant (N/m)

x = Distance of Compression or Expansion (m)

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