Polar Moment of Inertia of Hollow Circular Shaft Calculator

✖Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_outer]			+10% -10%
✖The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.ⓘ Inner Diameter of Shaft [d_inner]			+10% -10%

✖Polar Moment of Inertia of shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of Hollow Circular Shaft [J_shaft]

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Formula

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Polar Moment of Inertia of Hollow Circular Shaft

Formula

J shaft = \frac{π \cdot ({d outer}^{4} - {d inner}^{4})}{32}

Example

25.03457 m⁴ = \frac{π \cdot ({4000 mm}^{4} - {1000 mm}^{4})}{32}

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Polar Moment of Inertia of Hollow Circular Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32
J_shaft = (pi*(d_outer^(4)-d_inner^(4)))/32
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Polar Moment of Inertia of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.
Inner Diameter of Shaft - (Measured in Meter) - The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Shaft: 4000 Millimeter --> 4 Meter (Check conversion here)
Inner Diameter of Shaft: 1000 Millimeter --> 1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J_shaft = (pi*(d_outer^(4)-d_inner^(4)))/32 --> (pi*(4^(4)-1^(4)))/32

Evaluating ... ...

J_shaft = 25.0345664582937

STEP 3: Convert Result to Output's Unit

25.0345664582937 Meter⁴ --> No Conversion Required

FINAL ANSWER

25.0345664582937 ≈ 25.03457 Meter⁴ <-- Polar Moment of Inertia of shaft

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Shafts » Mechanical » Design of Hollow Shaft » Polar Moment of Inertia of Hollow Circular Shaft

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< Design of Hollow Shaft Calculators

Tensile Stress in Hollow Shaft when Subjected to Axial Force

Go Tensile Stress in Hollow Shaft = Axial Force on Hollow Shaft/(pi/4*(Outer Diameter of Hollow Shaft^2-Inner Diameter of Hollow Shaft^2))

Inner Diameter of Hollow Shaft given Ratio of Diameters

Go Inner Diameter of Hollow Shaft = Ratio of Inner to Outer Diameter of Hollow Shaft*Outer Diameter of Hollow Shaft

Ratio of Inner Diameter to Outer Diameter

Go Ratio of Inner to Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Outer Diameter of Hollow Shaft

Outer Diameter given Ratio of Diameters

Go Outer Diameter of Hollow Shaft = Inner Diameter of Hollow Shaft/Ratio of Inner to Outer Diameter of Hollow Shaft

Polar Moment of Inertia of Hollow Circular Shaft Formula

Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32
J_shaft = (pi*(d_outer^(4)-d_inner^(4)))/32

Define polar moment of inertia?

Polar Moment of Inertia is a measure of an object’s capacity to oppose or resist torsion when some amount of torque is applied to it on a specified axis. Torsion, on the other hand, is nothing but the twisting of an object due to an applied torque. Polar moment of inertia basically describes the cylindrical object’s (including its segments) resistance to torsional deformation when torque is applied in a plane that is parallel to the cross-section area or in a plane that is perpendicular to the object’s central axis.

How to Calculate Polar Moment of Inertia of Hollow Circular Shaft?

Polar Moment of Inertia of Hollow Circular Shaft calculator uses Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32 to calculate the Polar Moment of Inertia of shaft, The Polar moment of inertia of hollow circular shaft formula is a quantity used to describe resistance to torsional deformation, 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 of shaft is denoted by J_shaft symbol.

How to calculate Polar Moment of Inertia of Hollow Circular Shaft using this online calculator? To use this online calculator for Polar Moment of Inertia of Hollow Circular Shaft, enter Outer Diameter of Shaft (d_outer) & Inner Diameter of Shaft (d_inner) and hit the calculate button. Here is how the Polar Moment of Inertia of Hollow Circular Shaft calculation can be explained with given input values -> 25.03457 = (pi*(4^(4)-1^(4)))/32.

FAQ

What is Polar Moment of Inertia of Hollow Circular Shaft?

The Polar moment of inertia of hollow circular shaft formula is a quantity used to describe resistance to torsional deformation, 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_shaft = (pi*(d_outer^(4)-d_inner^(4)))/32 or Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32. Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft & The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

How to calculate Polar Moment of Inertia of Hollow Circular Shaft?

The Polar moment of inertia of hollow circular shaft formula is a quantity used to describe resistance to torsional deformation, 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 of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32. To calculate Polar Moment of Inertia of Hollow Circular Shaft, you need Outer Diameter of Shaft (d_outer) & Inner Diameter of Shaft (d_inner). With our tool, you need to enter the respective value for Outer Diameter of Shaft & Inner Diameter of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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