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Polar moment of inertia of shaft Formula

GoPolar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Formula

GoPolar moment of inertia of shaft given torque transmitted by shaft Formula

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Polar Moment of Inertia of shaft is the measure of object resistance to torsion. Check FAQs

J shaft = \frac{π \cdot {d s}^{4}}{32}

J_shaft - Polar Moment of Inertia of shaft?d_s - Diameter of Shaft?π - Archimedes' constant?

Polar moment of inertia of shaft Example

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Here is how the Polar moment of inertia of shaft equation looks like with Values.

Here is how the Polar moment of inertia of shaft equation looks like with Units.

Here is how the Polar moment of inertia of shaft equation looks like.

0.2036 = \frac{3.1416 \cdot 1200^{4}}{32}

0.2036m⁴ = \frac{3.1416 \cdot {1200mm}^{4}}{32}

0.2036 = \frac{3.1416 \cdot 1200^{4}}{32}

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Polar moment of inertia of shaft Solution

Follow our step by step solution on how to calculate Polar moment of inertia of shaft?

FIRST Step Consider the formula

J shaft = \frac{π \cdot {d s}^{4}}{32}

Next Step Substitute values of Variables

∴

J shaft = \frac{π \cdot {1200mm}^{4}}{32}

Next Step Substitute values of Constants

∴

J shaft = \frac{3.1416 \cdot {1200mm}^{4}}{32}

Next Step Convert Units

∴

J shaft = \frac{3.1416 \cdot {1.2m}^{4}}{32}

Next Step Prepare to Evaluate

∴

J shaft = \frac{3.1416 \cdot {1.2}^{4}}{32}

Next Step Evaluate

∴

J shaft = 0.203575203952619m⁴

LAST Step Rounding Answer

∴

J shaft = 0.2036m⁴

Polar moment of inertia of shaft Formula Elements

Variables

Constants

Polar Moment of Inertia of shaft

Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

Symbol: J_shaft

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia of shaft

Diameter of Shaft

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.

Symbol: d_s

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Polar Moment of Inertia of shaft

Go Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity

J shaft = \frac{τ \cdot L}{C \cdot θ}

Go Polar moment of inertia of shaft given torque transmitted by shaft

J shaft = \frac{τ \cdot R shaft}{𝜏 max}

Other formulas in Expression for Torque in terms of Polar Moment of Inertia category

Go Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia

C = \frac{τ \cdot L}{θ \cdot J shaft}

Go Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity

L = \frac{C \cdot θ \cdot J shaft}{τ}

Go Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity

θ = \frac{τ \cdot L}{C \cdot J shaft}

Go Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity

τ = \frac{C \cdot θ \cdot J shaft}{L}

How to Evaluate Polar moment of inertia of shaft?

Polar moment of inertia of shaft evaluator uses Polar Moment of Inertia of shaft = (pi*Diameter of Shaft^4)/32 to evaluate the Polar Moment of Inertia of shaft, The Polar moment of inertia of 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 of shaft is denoted by J_shaft symbol.

How to evaluate Polar moment of inertia of shaft using this online evaluator? To use this online evaluator for Polar moment of inertia of shaft, enter Diameter of Shaft (d_s) and hit the calculate button.

FAQs on Polar moment of inertia of shaft

What is the formula to find Polar moment of inertia of shaft?

The formula of Polar moment of inertia of shaft is expressed as Polar Moment of Inertia of shaft = (pi*Diameter of Shaft^4)/32. Here is an example- 0.203575 = (pi*1.2^4)/32.

How to calculate Polar moment of inertia of shaft?

With Diameter of Shaft (d_s) we can find Polar moment of inertia of shaft using the formula - Polar Moment of Inertia of shaft = (pi*Diameter of Shaft^4)/32. This formula also uses Archimedes' constant .

What are the other ways to Calculate Polar Moment of Inertia of shaft?

Here are the different ways to Calculate Polar Moment of Inertia of shaft-

Polar Moment of Inertia of shaft=(Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist)
Polar Moment of Inertia of shaft=(Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft

Can the Polar moment of inertia of shaft be negative?

Yes, the Polar moment of inertia of shaft, measured in Second Moment of Area can be negative.

Which unit is used to measure Polar moment of inertia of shaft?

Polar moment of inertia of shaft is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Polar moment of inertia of shaft can be measured.

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