Polar moment of inertia Calculator

✖Torque is a measure of the force that can cause an object to rotate about an axis.ⓘ Torque [T]			+10% -10%
✖Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%
✖Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.ⓘ Angle of Twist [θ]			+10% -10%
✖Modulus of Rigidity 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 [G_Torsion]			+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 [J]

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Polar moment of inertia Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)
J = (T*L_shaft)/(θ*G_Torsion)
This formula uses 5 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.
Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance between two ends of shaft.
Angle of Twist - (Measured in Radian) - Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity 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

Torque: 28 Kilonewton Meter --> 28000 Newton Meter (Check conversion here)
Length of Shaft: 4.58 Meter --> 4.58 Meter No Conversion Required
Angle of Twist: 1.42 Radian --> 1.42 Radian No Conversion Required
Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = (T*L_shaft)/(θ*G_Torsion) --> (28000*4.58)/(1.42*40000000000)

Evaluating ... ...

J = 2.25774647887324E-06

STEP 3: Convert Result to Output's Unit

2.25774647887324E-06 Meter⁴ --> No Conversion Required

FINAL ANSWER

2.25774647887324E-06 ≈ 2.3E-6 Meter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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< Torsion Calculators

Maximum permissible shear stress for given Radius and modulus of rigidity

LaTeX Go Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft

Twisting Moment given Maximum Permissible Shear Stress

LaTeX Go Torque = (Polar Moment of Inertia*Maximum Shear Stress)/Radius of Shaft

Radius with known Maximum permissible shear stress

LaTeX Go Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque

Maximum permissible shear stress

LaTeX Go Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia

Polar moment of inertia Formula

LaTeX Go

Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)
J = (T*L_shaft)/(θ*G_Torsion)

What is Torsion?

n 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.

How to Calculate Polar moment of inertia?

Polar moment of inertia calculator uses Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity) to calculate the Polar Moment of Inertia, The Polar moment of inertia is defined as when Shaft length, Twisting Moment, Modulus of rigidity, and Twist angle the resistance towards torsion. Polar Moment of Inertia is denoted by J symbol.

How to calculate Polar moment of inertia using this online calculator? To use this online calculator for Polar moment of inertia, enter Torque (T), Length of Shaft (L_shaft), Angle of Twist (θ) & Modulus of Rigidity (G_Torsion) and hit the calculate button. Here is how the Polar moment of inertia calculation can be explained with given input values -> 2.3E-6 = (28000*4.58)/(1.42*40000000000).

FAQ

What is Polar moment of inertia?

The Polar moment of inertia is defined as when Shaft length, Twisting Moment, Modulus of rigidity, and Twist angle the resistance towards torsion and is represented as J = (T*L_shaft)/(θ*G_Torsion) or Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity). Torque is a measure of the force that can cause an object to rotate about an axis, Length of Shaft is the distance between two ends of shaft, Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end & Modulus of Rigidity 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?

The Polar moment of inertia is defined as when Shaft length, Twisting Moment, Modulus of rigidity, and Twist angle the resistance towards torsion is calculated using Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity). To calculate Polar moment of inertia, you need Torque (T), Length of Shaft (L_shaft), Angle of Twist (θ) & Modulus of Rigidity (G_Torsion). With our tool, you need to enter the respective value for Torque, Length of Shaft, Angle of Twist & Modulus of Rigidity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Polar Moment of Inertia?

In this formula, Polar Moment of Inertia uses Torque, Length of Shaft, Angle of Twist & Modulus of Rigidity. We can use 2 other way(s) to calculate the same, which is/are as follows -

Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress
Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)

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