Polar Moment of Inertia given Torsional Section Modulus Calculator

✖The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.ⓘ Polar Modulus [Z_p]			+10% -10%
✖The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.ⓘ Radius of Shaft [R]			+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 given Torsional Section Modulus [J]

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Formula

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Polar Moment of Inertia given Torsional Section Modulus

Formula

`"J" = "Z"_{"p"}*"R"`

Example

`"0.000495m⁴"="4.5e-3m³"*"110mm"`

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Download Torsional Rigidity and Polar Modulus Formulas PDF

Polar Moment of Inertia given Torsional Section Modulus Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = Polar Modulus*Radius of Shaft
J = Z_p*R
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.
Polar Modulus - (Measured in Cubic Meter) - The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.
Radius of Shaft - (Measured in Meter) - The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

STEP 1: Convert Input(s) to Base Unit

Polar Modulus: 0.0045 Cubic Meter --> 0.0045 Cubic Meter No Conversion Required
Radius of Shaft: 110 Millimeter --> 0.11 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = Z_p*R --> 0.0045*0.11

Evaluating ... ...

J = 0.000495

STEP 3: Convert Result to Output's Unit

0.000495 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.000495 Meter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Strength of Materials » Torsion » Torsional Rigidity and Polar Modulus » Polar Modulus » Polar Moment of Inertia given Torsional Section Modulus

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< 9 Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus

Go Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4)

Polar Modulus of Hollow Shaft

Go Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)

Polar Moment of Inertia given Torsional Section Modulus

Go Polar Moment of Inertia = Polar Modulus*Radius of Shaft

Polar Moment of Inertia using Polar Modulus

Go Polar Moment of Inertia = Radius of Shaft*Polar Modulus

Polar Modulus

Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Polar Moment of Inertia of Solid Shaft

Go Polar Moment of Inertia = (pi*Dia of Shaft^4)/32

Diameter of Solid Shaft with known Polar Modulus

Go Dia of Shaft = ((16*Polar Modulus)/pi)^(1/3)

Polar Modulus using Maximum Twisting Moment

Go Polar Modulus = (Torque/Maximum Shear Stress)

Polar Modulus of Solid Shaft

Go Polar Modulus = (pi*Dia of Shaft^3)/16

Polar Moment of Inertia given Torsional Section Modulus Formula

Polar Moment of Inertia = Polar Modulus*Radius of Shaft
J = Z_p*R

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.

How to Calculate Polar Moment of Inertia given Torsional Section Modulus?

Polar Moment of Inertia given Torsional Section Modulus calculator uses Polar Moment of Inertia = Polar Modulus*Radius of Shaft to calculate the Polar Moment of Inertia, The Polar Moment of Inertia given Torsional Section Modulus is defined as the moment of inertia of the cross-section when its undergoing twisting. Polar Moment of Inertia is denoted by J symbol.

How to calculate Polar Moment of Inertia given Torsional Section Modulus using this online calculator? To use this online calculator for Polar Moment of Inertia given Torsional Section Modulus, enter Polar Modulus (Z_p) & Radius of Shaft (R) and hit the calculate button. Here is how the Polar Moment of Inertia given Torsional Section Modulus calculation can be explained with given input values -> 0.000495 = 0.0045*0.11.

FAQ

What is Polar Moment of Inertia given Torsional Section Modulus?

The Polar Moment of Inertia given Torsional Section Modulus is defined as the moment of inertia of the cross-section when its undergoing twisting and is represented as J = Z_p*R or Polar Moment of Inertia = Polar Modulus*Radius of Shaft. The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp & The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

How to calculate Polar Moment of Inertia given Torsional Section Modulus?

The Polar Moment of Inertia given Torsional Section Modulus is defined as the moment of inertia of the cross-section when its undergoing twisting is calculated using Polar Moment of Inertia = Polar Modulus*Radius of Shaft. To calculate Polar Moment of Inertia given Torsional Section Modulus, you need Polar Modulus (Z_p) & Radius of Shaft (R). With our tool, you need to enter the respective value for Polar Modulus & Radius of Shaft 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 Polar Modulus & Radius of Shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -

Polar Moment of Inertia = Radius of Shaft*Polar Modulus
Polar Moment of Inertia = (pi*Dia of Shaft^4)/32

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