Polar Modulus Calculator

✖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]			+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%

✖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]

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Polar Modulus Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Modulus = Polar Moment of Inertia/Radius of Shaft
Z_p = J/R
This formula uses 3 Variables

Variables Used

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.
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.
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 Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Radius of Shaft: 110 Millimeter --> 0.11 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z_p = J/R --> 0.0041/0.11

Evaluating ... ...

Z_p = 0.0372727272727273

STEP 3: Convert Result to Output's Unit

0.0372727272727273 Cubic Meter --> No Conversion Required

FINAL ANSWER

0.0372727272727273 ≈ 0.037273 Cubic Meter <-- Polar Modulus

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Polar Modulus Calculators

Polar Moment of Inertia using Polar Modulus

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

Radius of Shaft using Polar Modulus

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

Polar Modulus

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

Polar Moment of Inertia of Solid Shaft

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

< Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus

LaTeX 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

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

Polar Modulus

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

Diameter of Solid Shaft with known Polar Modulus

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

Polar Modulus Formula

LaTeX Go

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

What is difference between Moment of Inertia and Polar Moment of Inertia?

The Main difference between the moment of inertia and the polar moment of inertia is that the moment of inertia measures how an object resists angular acceleration, whereas the polar moment of inertia measures how an object resists torsion.

How to Calculate Polar Modulus?

Polar Modulus calculator uses Polar Modulus = Polar Moment of Inertia/Radius of Shaft to calculate the Polar Modulus, The Polar Modulus formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called a torsional section modulus. It is denoted by Z p. Polar Modulus is denoted by Z_p symbol.

How to calculate Polar Modulus using this online calculator? To use this online calculator for Polar Modulus, enter Polar Moment of Inertia (J) & Radius of Shaft (R) and hit the calculate button. Here is how the Polar Modulus calculation can be explained with given input values -> 0.037273 = 0.0041/0.11.

FAQ

What is Polar Modulus?

The Polar Modulus formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called a torsional section modulus. It is denoted by Z p and is represented as Z_p = J/R or Polar Modulus = Polar Moment of Inertia/Radius of Shaft. 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 & 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 Modulus?

The Polar Modulus formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called a torsional section modulus. It is denoted by Z p is calculated using Polar Modulus = Polar Moment of Inertia/Radius of Shaft. To calculate Polar Modulus, you need Polar Moment of Inertia (J) & Radius of Shaft (R). With our tool, you need to enter the respective value for Polar Moment of Inertia & 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 Modulus?

In this formula, Polar Modulus uses Polar Moment of Inertia & Radius of Shaft. We can use 3 other way(s) to calculate the same, which is/are as follows -

Polar Modulus = (pi*Dia of Shaft^3)/16
Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)

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