Length

List of relevant formulas below for:

  • Variables : Length

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)

Volume of a Pyramid

 , where:

V = Volume of a Pyramid

a = Length of Base

b = Width of Base

h = Height of Pyramid

Area of a Trapezoid

 , where:

A = Area of a Trapezoid

h = Height of Trapezoid

a = Length of Lower Base

b = Lenght of Lower Base

m = Length of Median

Volume of a Cube

 , where:

V = Volume of a Cube

a = Length of Cube

b = Height of Cube

c = Width of Cube

Lorentz Contraction

 , where:

L' = Observed Length (m)

L = Proper Length in Rest Frame (m)

 = Lorentz Factor

Electromotive Force (emf)

 , where:

 = Electromotve Force (V)

E = Electric Field algined with path between A and B (Conservative Electrostatic Field) (N/C)

 = Dot Product

L = Elemental length of path between A and B

Biot-Savart Law

Magnetic field created by a current:

 , where:

B = Magnetic B-Field (T)

 = Magnetic Constant (H/m), written as mu nought (u0)

 = Pi

I = Current (A)

Ampère's Circuital Law

Also known as Ampère's Law with Maxwell's Correction,

  or

   , where:

 = Curl Operator

B = Magnetic B-Field (T)

Electrical Resistivity

 , where:

 = Electrical Resistivity (Ω*m)

R = Resistance (Ω)

A = Cross-Sectional Area (m2)

 = Length (m)

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