Polar Moment of Inertia of Solid Shaft Calculator

✖The Dia of Shaft is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.ⓘ Dia of Shaft [d]

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✖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 of Solid Shaft [J]

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Polar Moment of Inertia of Solid Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = (pi*Dia of Shaft^4)/32
J = (pi*d^4)/32
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Dia of Shaft - (Measured in Meter) - The Dia of Shaft is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.

STEP 1: Convert Input(s) to Base Unit

Dia of Shaft: 0.284 Meter --> 0.284 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = (pi*d^4)/32 --> (pi*0.284^4)/32

Evaluating ... ...

J = 0.000638665202759738

STEP 3: Convert Result to Output's Unit

0.000638665202759738 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.000638665202759738 ≈ 0.000639 Meter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Mechanical » Polar Modulus » Polar Moment of Inertia of Solid Shaft

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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 Moment of Inertia of Solid Shaft Formula

LaTeX Go

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

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 of Solid Shaft?

Polar Moment of Inertia of Solid Shaft calculator uses Polar Moment of Inertia = (pi*Dia of Shaft^4)/32 to calculate the Polar Moment of Inertia, The Polar Moment of Inertia of Solid Shaft 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 of Solid Shaft using this online calculator? To use this online calculator for Polar Moment of Inertia of Solid Shaft, enter Dia of Shaft (d) and hit the calculate button. Here is how the Polar Moment of Inertia of Solid Shaft calculation can be explained with given input values -> 0.000639 = (pi*0.284^4)/32.

FAQ

What is Polar Moment of Inertia of Solid Shaft?

The Polar Moment of Inertia of Solid Shaft 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 = (pi*d^4)/32 or Polar Moment of Inertia = (pi*Dia of Shaft^4)/32. The Dia of Shaft is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.

How to calculate Polar Moment of Inertia of Solid Shaft?

The Polar Moment of Inertia of Solid Shaft 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 = (pi*Dia of Shaft^4)/32. To calculate Polar Moment of Inertia of Solid Shaft, you need Dia of Shaft (d). With our tool, you need to enter the respective value for Dia 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 Dia of Shaft. We can use 3 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/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)
Polar Moment of Inertia = Radius of Shaft*Polar Modulus

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