Polar Moment of Inertia with Known Torsional Rigidity Calculator

✖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.ⓘ Torsional Rigidity [TJ]			+10% -10%
✖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.ⓘ Modulus of Rigidity SOM [G]			+10% -10%

✖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.ⓘ Polar Moment of Inertia with Known Torsional Rigidity [J]

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Formula

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Polar Moment of Inertia with Known Torsional Rigidity

Formula

`"J" = "TJ"/"G"`

Example

`"0.004105m⁴"="90.3kN*m²"/"0.022GPa"`

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Polar Moment of Inertia with Known Torsional Rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM
J = TJ/G
This formula uses 3 Variables

Variables Used

Polar Moment of Inertia - (Measured in Meter⁴) - 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.
Torsional Rigidity - (Measured in Newton Square Meter) - 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.
Modulus of Rigidity SOM - (Measured in Pascal) - 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.

STEP 1: Convert Input(s) to Base Unit

Torsional Rigidity: 90.3 Kilonewton Square Meter --> 90300 Newton Square Meter (Check conversion here)
Modulus of Rigidity SOM: 0.022 Gigapascal --> 22000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = TJ/G --> 90300/22000000

Evaluating ... ...

J = 0.00410454545454545

STEP 3: Convert Result to Output's Unit

0.00410454545454545 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.00410454545454545 ≈ 0.004105 Meter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< 7 Torsional Rigidity Calculators

Torsional Rigidity using Torque and Length of Shaft

Go Torsional Rigidity = (Torque*Length of Shaft)/Angle of Twist

Angle of Twist for Shaft using Torsional Rigidity

Go Angle of Twist = (Torque*Length of Shaft)/Torsional Rigidity

Torque on Shaft using Torsional Rigidity

Go Torque = (Torsional Rigidity*Angle of Twist)/Length of Shaft

Length of Shaft using Torsional Rigidity

Go Length of Shaft = (Torsional Rigidity*Angle of Twist)/Torque

Polar Moment of Inertia with Known Torsional Rigidity

Go Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM

Modulus of Rigidity with Known Torsional Rigidity

Go Modulus of Rigidity SOM = Torsional Rigidity/Polar Moment of Inertia

Torsional Rigidity

Go Torsional Rigidity = Modulus of Rigidity SOM*Polar Moment of Inertia

< 7 Torsional Rigidity Calculators

Torsional Rigidity using Torque and Length of Shaft

Go Torsional Rigidity = (Torque*Length of Shaft)/Angle of Twist

Angle of Twist for Shaft using Torsional Rigidity

Go Angle of Twist = (Torque*Length of Shaft)/Torsional Rigidity

Length of Shaft using Torsional Rigidity

Go Length of Shaft = (Torsional Rigidity*Angle of Twist)/Torque

Torque on Shaft using Torsional Rigidity

Go Torque = (Torsional Rigidity*Angle of Twist)/Length of Shaft

Polar Moment of Inertia with Known Torsional Rigidity

Go Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM

Modulus of Rigidity with Known Torsional Rigidity

Go Modulus of Rigidity SOM = Torsional Rigidity/Polar Moment of Inertia

Torsional Rigidity

Go Torsional Rigidity = Modulus of Rigidity SOM*Polar Moment of Inertia

Polar Moment of Inertia with Known Torsional Rigidity Formula

Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM
J = TJ/G

What is Torsion?

In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal, an SI unit for newtons per square metre, or in pounds per square inch while torque is expressed in newton metres or foot-pound force.

What is Torsional Rigidity?

Torsional rigidity, sometimes referred to as torsional stiffness, is the ability of an object to resist twisting when acted upon by an external force, torque.

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

Polar Moment of Inertia with Known Torsional Rigidity calculator uses Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM to calculate 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 calculate Polar Moment of Inertia with Known Torsional Rigidity using this online calculator? To use this online calculator for Polar Moment of Inertia with Known Torsional Rigidity, enter Torsional Rigidity (TJ) & Modulus of Rigidity SOM (G) and hit the calculate button. Here is how the Polar Moment of Inertia with Known Torsional Rigidity calculation can be explained with given input values -> 0.004105 = 90300/22000000.

FAQ

What is Polar Moment of Inertia with Known Torsional Rigidity?

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 and is represented as J = TJ/G or Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM. 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 & 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.

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

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 is calculated using Polar Moment of Inertia = Torsional Rigidity/Modulus of Rigidity SOM. To calculate Polar Moment of Inertia with Known Torsional Rigidity, you need Torsional Rigidity (TJ) & Modulus of Rigidity SOM (G). With our tool, you need to enter the respective value for Torsional Rigidity & Modulus of Rigidity SOM and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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