Polar Moment of Inertia of Hollow Shaft Calculator

✖Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_o]			+10% -10%
✖The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.ⓘ Inner Dia of Shaft [d_i]			+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 of Hollow Shaft [J]

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Polar Moment of Inertia of Hollow Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)
J = pi/32*(d_o^4-d_i^4)
This formula uses 1 Constants, 3 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.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.
Inner Dia of Shaft - (Measured in Meter) - The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Shaft: 700 Millimeter --> 0.7 Meter (Check conversion here)
Inner Dia of Shaft: 0.688 Meter --> 0.688 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = pi/32*(d_o^4-d_i^4) --> pi/32*(0.7^4-0.688^4)

Evaluating ... ...

J = 0.00157525912252214

STEP 3: Convert Result to Output's Unit

0.00157525912252214 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.00157525912252214 ≈ 0.001575 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 Hollow 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

< Torsion Calculators

Maximum permissible shear stress for given Radius and modulus of rigidity

LaTeX Go Maximum Shear Stress = (Modulus of Rigidity*(Angle of Twist)*Radius of Shaft)/Length of Shaft

Twisting Moment given Maximum Permissible Shear Stress

LaTeX Go Torque = (Polar Moment of Inertia*Maximum Shear Stress)/Radius of Shaft

Radius with known Maximum permissible shear stress

LaTeX Go Radius of Shaft = Maximum Shear Stress*Polar Moment of Inertia/Torque

Maximum permissible shear stress

LaTeX Go Maximum Shear Stress = Torque*Radius of Shaft/Polar Moment of Inertia

Polar Moment of Inertia of Hollow Shaft Formula

LaTeX Go

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

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 Hollow Shaft?

Polar Moment of Inertia of Hollow Shaft calculator uses Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4) to calculate the Polar Moment of Inertia, The Polar Moment of Inertia of Hollow 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 Hollow Shaft using this online calculator? To use this online calculator for Polar Moment of Inertia of Hollow Shaft, enter Outer Diameter of Shaft (d_o) & Inner Dia of Shaft (d_i) and hit the calculate button. Here is how the Polar Moment of Inertia of Hollow Shaft calculation can be explained with given input values -> 0.001575 = pi/32*(0.7^4-0.688^4).

FAQ

What is Polar Moment of Inertia of Hollow Shaft?

The Polar Moment of Inertia of Hollow 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/32*(d_o^4-d_i^4) or Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4). Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft & The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.

How to calculate Polar Moment of Inertia of Hollow Shaft?

The Polar Moment of Inertia of Hollow 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/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4). To calculate Polar Moment of Inertia of Hollow Shaft, you need Outer Diameter of Shaft (d_o) & Inner Dia of Shaft (d_i). With our tool, you need to enter the respective value for Outer Diameter of Shaft & Inner 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 Outer Diameter of Shaft & Inner 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*Dia of Shaft^4)/32
Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress

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