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Polar moment of inertia of circular cross section Formula

GoPolar moment of inertia of hollow circular cross-section Formula

GoPolar moment of inertia of shaft given shear stress and torsional moment Formula

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Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion. Check FAQs

J = π \cdot \frac{{d c}^{4}}{32}

J - Polar moment of inertia for circular section?d_c - Diameter of circular section of shaft?π - Archimedes' constant?

Polar moment of inertia of circular cross section Example

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Here is how the Polar moment of inertia of circular cross section equation looks like with Values.

Here is how the Polar moment of inertia of circular cross section equation looks like with Units.

Here is how the Polar moment of inertia of circular cross section equation looks like.

131194.48 = 3.1416 \cdot \frac{34^{4}}{32}

131194.48mm⁴ = 3.1416 \cdot \frac{{34mm}^{4}}{32}

131194.48 = 3.1416 \cdot \frac{34^{4}}{32}

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Polar moment of inertia of circular cross section Solution

Follow our step by step solution on how to calculate Polar moment of inertia of circular cross section?

FIRST Step Consider the formula

J = π \cdot \frac{{d c}^{4}}{32}

Next Step Substitute values of Variables

∴

J = π \cdot \frac{{34mm}^{4}}{32}

Next Step Substitute values of Constants

∴

J = 3.1416 \cdot \frac{{34mm}^{4}}{32}

Next Step Convert Units

∴

J = 3.1416 \cdot \frac{{0.034m}^{4}}{32}

Next Step Prepare to Evaluate

∴

J = 3.1416 \cdot \frac{{0.034}^{4}}{32}

Next Step Evaluate

∴

J = 1.31194480010237E-07m⁴

Next Step Convert to Output's Unit

∴

J = 131194.480010237mm⁴

LAST Step Rounding Answer

∴

J = 131194.48mm⁴

Polar moment of inertia of circular cross section Formula Elements

Variables

Constants

Polar moment of inertia for circular section

Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion.

Symbol: J

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Polar moment of inertia for circular section

Diameter of circular section of shaft

Diameter of circular section of shaft is the diameter of the circular cross-section of the specimen.

Symbol: d_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of circular section 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 for circular section

Go Polar moment of inertia of hollow circular cross-section

J = π \cdot \frac{({d ho}^{4}) - ({d hi}^{4})}{32}

Go Polar moment of inertia of shaft given shear stress and torsional moment

J = τ \cdot \frac{r}{𝜏}

Other formulas in Design of Shaft for Torsional Moment category

Go Torsional shear stress in shaft due to torsional moment

𝜏 = τ \cdot \frac{r}{J}

Go Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia

θ = \frac{τ \cdot l}{J \cdot C}

Go Angle of twist of solid cylindrical rod in degrees

𝜽 d = (584 \cdot τ \cdot \frac{l}{C \cdot ({d c}^{4})}) \cdot (\frac{π}{180})

Go Angle of twist of hollow cylindrical rod in degrees

𝜽 d = (584 \cdot τ \cdot \frac{l}{C \cdot (({d ho}^{4}) - ({d hi}^{4}))}) \cdot (\frac{π}{180})

How to Evaluate Polar moment of inertia of circular cross section?

Polar moment of inertia of circular cross section evaluator uses Polar moment of inertia for circular section = pi*(Diameter of circular section of shaft^4)/32 to evaluate the Polar moment of inertia for circular section, The Polar moment of inertia of circular cross section formula 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. Polar moment of inertia for circular section is denoted by J symbol.

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

FAQs on Polar moment of inertia of circular cross section

What is the formula to find Polar moment of inertia of circular cross section?

The formula of Polar moment of inertia of circular cross section is expressed as Polar moment of inertia for circular section = pi*(Diameter of circular section of shaft^4)/32. Here is an example- 1.3E+17 = pi*(0.034^4)/32.

How to calculate Polar moment of inertia of circular cross section?

With Diameter of circular section of shaft (d_c) we can find Polar moment of inertia of circular cross section using the formula - Polar moment of inertia for circular section = pi*(Diameter of circular section of shaft^4)/32. This formula also uses Archimedes' constant .

What are the other ways to Calculate Polar moment of inertia for circular section?

Here are the different ways to Calculate Polar moment of inertia for circular section-

Polar moment of inertia for circular section=pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32
Polar moment of inertia for circular section=Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft

Can the Polar moment of inertia of circular cross section be negative?

No, the Polar moment of inertia of circular cross section, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar moment of inertia of circular cross section?

Polar moment of inertia of circular cross section is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Polar moment of inertia of circular cross section can be measured.

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