# Statics

## 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:

, 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:

$J = b* h^3/12$, 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:

$J = b^4/12$ , 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)