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Polar Moment of Inertia with Known Torsional Rigidity Formula

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Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section. Check FAQs

J = \frac{TJ}{G}

J - Polar Moment of Inertia?TJ - Torsional Rigidity?G - Modulus of Rigidity SOM?

Polar Moment of Inertia with Known Torsional Rigidity Example

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Here is how the Polar Moment of Inertia with Known Torsional Rigidity equation looks like with Values.

Here is how the Polar Moment of Inertia with Known Torsional Rigidity equation looks like with Units.

Here is how the Polar Moment of Inertia with Known Torsional Rigidity equation looks like.

0.0041 = \frac{90.3}{0.022}

0.0041m⁴ = \frac{90.3kN*m²}{0.022GPa}

0.0041 = \frac{90.3}{0.022}

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Polar Moment of Inertia with Known Torsional Rigidity Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia with Known Torsional Rigidity?

FIRST Step Consider the formula

J = \frac{TJ}{G}

Next Step Substitute values of Variables

∴

J = \frac{90.3kN*m²}{0.022GPa}

Next Step Convert Units

∴

J = \frac{90300N*m²}{2.2E+7Pa}

Next Step Prepare to Evaluate

∴

J = \frac{90300}{2.2E+7}

Next Step Evaluate

∴

J = 0.00410454545454545m⁴

LAST Step Rounding Answer

∴

J = 0.0041m⁴

Polar Moment of Inertia with Known Torsional Rigidity Formula Elements

Variables

Polar Moment of Inertia

Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Torsional Rigidity

Torsional Rigidity is defined as how much an object of specified material resists twisting force, also known as torque. It is based on both the material of the object, as well as its shape.

Symbol: TJ

Measurement: Torsional RigidityUnit: kN*m²

Note: Value can be positive or negative.

Formulas to find Torsional Rigidity

Modulus of Rigidity SOM

Modulus of Rigidity SOM is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

Symbol: G

Measurement: PressureUnit: GPa

Note: Value can be positive or negative.

Formulas to find Modulus of Rigidity SOM

Other formulas in Torsional Rigidity category

Go Angle of Twist for Shaft using Torsional Rigidity

θ = \frac{T \cdot L shaft}{TJ}

Go Length of Shaft using Torsional Rigidity

L shaft = \frac{TJ \cdot θ}{T}

Go Modulus of Rigidity with Known Torsional Rigidity

G = \frac{TJ}{J}

Go Torque on Shaft using Torsional Rigidity

T = \frac{TJ \cdot θ}{L shaft}

How to Evaluate Polar Moment of Inertia with Known Torsional Rigidity?

Polar Moment of Inertia with Known Torsional Rigidity evaluator uses Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia with known Torsional Rigidity formula is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation. Polar Moment of Inertia is denoted by J symbol.

How to evaluate Polar Moment of Inertia with Known Torsional Rigidity using this online evaluator? To use this online evaluator for Polar Moment of Inertia with Known Torsional Rigidity, enter Torsional Rigidity (TJ) & Modulus of Rigidity SOM (G) and hit the calculate button.

FAQs on Polar Moment of Inertia with Known Torsional Rigidity

What is the formula to find Polar Moment of Inertia with Known Torsional Rigidity?

The formula of Polar Moment of Inertia with Known Torsional Rigidity is expressed as Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM. Here is an example- 0.004105 = 90300/22000000.

How to calculate Polar Moment of Inertia with Known Torsional Rigidity?

With Torsional Rigidity (TJ) & Modulus of Rigidity SOM (G) we can find Polar Moment of Inertia with Known Torsional Rigidity using the formula - Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM.

Can the Polar Moment of Inertia with Known Torsional Rigidity be negative?

No, the Polar Moment of Inertia with Known Torsional Rigidity, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar Moment of Inertia with Known Torsional Rigidity?

Polar Moment of Inertia with Known Torsional Rigidity is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Polar Moment of Inertia with Known Torsional Rigidity can be measured.

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