Statics

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Gravitational Potential Energy

 , where:

E = Gravitational Potential Energy (J)

m = Mass (kg)

g = Gravity (m/s^2)

h = Height (m)

Impact Shear on a Bar

 , where:

 = Shear Stress (Pa)

U = Change in Kinetic Energy upon Impact (J)

G = Shear Modulus (Pa)

V = Volume of Rod (m^3)

Poisson Ratio

Property of a material when stretched along axial direction.

 , where:

 = Poisson's Ratio

 = Strain in Given Direction

Polar Moment of Inertia

This is the general formula for the polar moment of inertia, also known as the second moment of area.  It can be applied to find the polar moment of inertia of a circle segment, the polar moment of inertia of a cylinder, or the polar moment of inertia of a rectangle.  Most shapes have specific, easier to follow formulas.  The units, english and imperial, are length to the fourth (m^4 or ft^4).

 , where:

Polar Moment of Inertia of a Circle

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

 , where:

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

 = pi, 3.1415...

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