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Polar Moment of Inertia given Torsional Section Modulus Formula

GoPolar Moment of Inertia using Polar Modulus Formula

GoPolar Moment of Inertia of Solid Shaft Formula

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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. Check FAQs

J = Z p \cdot R

J - Polar Moment of Inertia?Z_p - Polar Modulus?R - Radius of Shaft?

Polar Moment of Inertia given Torsional Section Modulus Example

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Here is how the Polar Moment of Inertia given Torsional Section Modulus equation looks like with Values.

Here is how the Polar Moment of Inertia given Torsional Section Modulus equation looks like with Units.

Here is how the Polar Moment of Inertia given Torsional Section Modulus equation looks like.

0.0005 = 0.0045 \cdot 110

0.0005m⁴ = 0.0045m³ \cdot 110mm

0.0005 = 0.0045 \cdot 110

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Polar Moment of Inertia given Torsional Section Modulus Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia given Torsional Section Modulus?

FIRST Step Consider the formula

J = Z p \cdot R

Next Step Substitute values of Variables

∴

J = 0.0045m³ \cdot 110mm

Next Step Convert Units

∴

J = 0.0045m³ \cdot 0.11m

Next Step Prepare to Evaluate

∴

J = 0.0045 \cdot 0.11

Next Step Evaluate

∴

J = 0.000495m⁴

LAST Step Rounding Answer

∴

J = 0.0005m⁴

Polar Moment of Inertia given Torsional Section Modulus Formula Elements

Variables

Polar Moment of Inertia

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.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Polar Modulus

The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.

Symbol: Z_p

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Polar Modulus

Radius of Shaft

The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Shaft

Other Formulas to find Polar Moment of Inertia

Go Polar Moment of Inertia using Polar Modulus

J = R \cdot Z p

Go Polar Moment of Inertia of Solid Shaft

J = \frac{π \cdot d^{4}}{32}

Other formulas in Polar Modulus category

Go Diameter of Solid Shaft with known Polar Modulus

d = {(\frac{16 \cdot Z p}{π})}^{\frac{1}{3}}

Go Inner diameter of Hollow Shaft using Polar Modulus

d i = {(({d o}^{4}) - (\frac{Z p \cdot 16 \cdot d o}{π}))}^{\frac{1}{4}}

Go Polar Modulus

Z p = \frac{J}{R}

Go Polar Modulus of Hollow Shaft

Z p = \frac{π \cdot (({d o}^{4}) - ({d i}^{4}))}{16 \cdot d o}

How to Evaluate Polar Moment of Inertia given Torsional Section Modulus?

Polar Moment of Inertia given Torsional Section Modulus evaluator uses Polar Moment of Inertia = Polar Modulus*Radius of Shaft to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia given Torsional Section Modulus is defined as the moment of inertia of the cross-section when its undergoing twisting. Polar Moment of Inertia is denoted by J symbol.

How to evaluate Polar Moment of Inertia given Torsional Section Modulus using this online evaluator? To use this online evaluator for Polar Moment of Inertia given Torsional Section Modulus, enter Polar Modulus (Z_p) & Radius of Shaft (R) and hit the calculate button.

FAQs on Polar Moment of Inertia given Torsional Section Modulus

What is the formula to find Polar Moment of Inertia given Torsional Section Modulus?

The formula of Polar Moment of Inertia given Torsional Section Modulus is expressed as Polar Moment of Inertia = Polar Modulus*Radius of Shaft. Here is an example- 0.000495 = 0.0045*0.11.

How to calculate Polar Moment of Inertia given Torsional Section Modulus?

With Polar Modulus (Z_p) & Radius of Shaft (R) we can find Polar Moment of Inertia given Torsional Section Modulus using the formula - Polar Moment of Inertia = Polar Modulus*Radius of Shaft.

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

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

Polar Moment of Inertia=Radius of Shaft*Polar Modulus
Polar Moment of Inertia=(pi*Dia of Shaft^4)/32

Can the Polar Moment of Inertia given Torsional Section Modulus be negative?

No, the Polar Moment of Inertia given Torsional Section Modulus, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar Moment of Inertia given Torsional Section Modulus?

Polar Moment of Inertia given Torsional Section Modulus 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 given Torsional Section Modulus can be measured.

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Polar Moment of Inertia given Torsional Section Modulus Formula

​GoPolar Moment of Inertia using Polar Modulus Formula

​GoPolar Moment of Inertia of Solid Shaft Formula

Polar Moment of Inertia given Torsional Section Modulus Example

Polar Moment of Inertia given Torsional Section Modulus Solution

Polar Moment of Inertia given Torsional Section Modulus Formula Elements

Other Formulas to find Polar Moment of Inertia

Other formulas in Polar Modulus category

How to Evaluate Polar Moment of Inertia given Torsional Section Modulus?

FAQs on Polar Moment of Inertia given Torsional Section Modulus

Variable Name

GoPolar Moment of Inertia using Polar Modulus Formula

GoPolar Moment of Inertia of Solid Shaft Formula