Moment of Inertia about Polar Axis Calculator

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

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✖The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.ⓘ Moment of Inertia about Polar Axis [J]

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Formula

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Moment of Inertia about Polar Axis

Formula

`"J" = (pi*"d"_{"s"}^(4))/32`

Example

`"0.203575m⁴"=(pi*("1200mm")^(4))/32`

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Moment of Inertia about Polar Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32
J = (pi*d_s^(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) - The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.
Diameter of Shaft - (Measured in Meter) - The Diameter 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

Diameter of Shaft: 1200 Millimeter --> 1.2 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J = (pi*d_s^(4))/32 --> (pi*1.2^(4))/32

Evaluating ... ...

J = 0.203575203952619

STEP 3: Convert Result to Output's Unit

0.203575203952619 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.203575203952619 ≈ 0.203575 Meter⁴ <-- Polar Moment of Inertia

(Calculation completed in 00.004 seconds)

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Created by Pragati Jaju

College Of Engineering (COEP), Pune

Pragati Jaju has created this Calculator and 50+ more calculators!

Verified by Kethavath Srinath

Osmania University (OU), Hyderabad

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< 18 Stress and Strain Calculators

Elongation Circular Tapered Bar

Go Elongation = (4*Load*Length of Bar)/(pi*Diameter of Bigger End*Diameter of Smaller End*Elastic Modulus)

Total Angle of Twist

Go Total Angle of Twist = (Torque Exerted on Wheel*Shaft Length)/(Shear Modulus*Polar Moment of Inertia)

Moment of Inertia for Hollow Circular Shaft

Go Polar Moment of Inertia = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4))

Equivalent Bending Moment

Go Equivalent Bending Moment = Bending Moment+sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Deflection of Fixed Beam with Uniformly Distributed Load

Go Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia)

Deflection of Fixed Beam with Load at Center

Go Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia)

Elongation of Prismatic Bar due to its Own Weight

Go Elongation = (2*Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Axial Elongation of Prismatic Bar due to External Load

Go Elongation = (Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)

Hooke's Law

Go Young's Modulus = (Load*Elongation)/(Area of Base*Initial Length)

Equivalent Torsional Moment

Go Equivalent Torsion Moment = sqrt(Bending Moment^(2)+Torque Exerted on Wheel^(2))

Rankine's Formula for Columns

Go Rankine’s Critical Load = 1/(1/Euler’s Buckling Load+1/Ultimate Crushing Load for Columns)

Slenderness Ratio

Go Slenderness Ratio = Effective Length/Least Radius of Gyration

Moment of Inertia about Polar Axis

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

Bulk Modulus given Volume Stress and Strain

Go Bulk Modulus = Volume Stress/Volumetric Strain

Shear Modulus

Go Shear Modulus = Shear Stress/Shear Strain

Bulk Modulus given Bulk Stress and Strain

Go Bulk Modulus = Bulk Stress/Bulk Strain

Young's Modulus

Go Young's Modulus = Stress/Strain

Elastic Modulus

Go Young's Modulus = Stress/Strain

Moment of Inertia about Polar Axis Formula

Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32
J = (pi*d_s^(4))/32

What is 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 Moment of Inertia about Polar Axis?

Moment of Inertia about Polar Axis calculator uses Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32 to calculate the Polar Moment of Inertia, The Moment of Inertia about Polar Axis is a shaft or beam's resistance to being distorted by torsion, as a function of its shape. Polar Moment of Inertia is denoted by J symbol.

How to calculate Moment of Inertia about Polar Axis using this online calculator? To use this online calculator for Moment of Inertia about Polar Axis, enter Diameter of Shaft (d_s) and hit the calculate button. Here is how the Moment of Inertia about Polar Axis calculation can be explained with given input values -> 0.203575 = (pi*1.2^(4))/32.

FAQ

What is Moment of Inertia about Polar Axis?

The Moment of Inertia about Polar Axis is a shaft or beam's resistance to being distorted by torsion, as a function of its shape and is represented as J = (pi*d_s^(4))/32 or Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32. The Diameter 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 Moment of Inertia about Polar Axis?

The Moment of Inertia about Polar Axis is a shaft or beam's resistance to being distorted by torsion, as a function of its shape is calculated using Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32. To calculate Moment of Inertia about Polar Axis, you need Diameter of Shaft (d_s). With our tool, you need to enter the respective value for Diameter 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 Diameter of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

Polar Moment of Inertia = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4))

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