Polar Moment of Inertia using Polar Modulus Calculator

✖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]			+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 using Polar Modulus [J]

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Polar Moment of Inertia using Polar Modulus

Formula

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

Example

`"0.000495m⁴"="110mm"*"4.5e-3m³"`

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Download Torsion of Shafts And Springs Formula PDF

Polar Moment of Inertia using Polar Modulus Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = R*Z_p --> 0.11*0.0045

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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National Institute Of Technology (NIT), Hamirpur

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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 of Hollow Shaft

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

Polar Moment of Inertia using Polar Modulus

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

Radius of Shaft using Polar Modulus

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

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

< 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 using Polar Modulus Formula

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

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 Moment of Inertia using Polar Modulus?

Polar Moment of Inertia using Polar Modulus calculator uses Polar Moment of Inertia = Radius of Shaft*Polar Modulus to calculate the Polar Moment of Inertia, The Polar Moment of Inertia using Polar Modulus formula is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the 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 using Polar Modulus using this online calculator? To use this online calculator for Polar Moment of Inertia using Polar Modulus, enter Radius of Shaft (R) & Polar Modulus (Z_p) and hit the calculate button. Here is how the Polar Moment of Inertia using Polar Modulus calculation can be explained with given input values -> 0.000495 = 0.11*0.0045.

FAQ

What is Polar Moment of Inertia using Polar Modulus?

The Polar Moment of Inertia using Polar Modulus formula is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation and is represented as J = R*Z_p or Polar Moment of Inertia = Radius of Shaft*Polar Modulus. The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface & 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.

How to calculate Polar Moment of Inertia using Polar Modulus?

The Polar Moment of Inertia using Polar Modulus formula is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation is calculated using Polar Moment of Inertia = Radius of Shaft*Polar Modulus. To calculate Polar Moment of Inertia using Polar Modulus, you need Radius of Shaft (R) & Polar Modulus (Z_p). With our tool, you need to enter the respective value for Radius of Shaft & Polar Modulus 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 Radius of Shaft & Polar Modulus. We can use 4 other way(s) to calculate the same, which is/are as follows -

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

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