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Polar Moment of Inertia using Polar Modulus Formula

GoPolar Moment of Inertia of Solid Shaft Formula

GoPolar Moment of Inertia given Torsional Section Modulus 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 = R \cdot Z p

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

Polar Moment of Inertia using Polar Modulus Example

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Here is how the Polar Moment of Inertia using Polar Modulus equation looks like with Values.

Here is how the Polar Moment of Inertia using Polar Modulus equation looks like with Units.

Here is how the Polar Moment of Inertia using Polar Modulus equation looks like.

0.0005 = 110 \cdot 0.0045

0.0005m⁴ = 110mm \cdot 0.0045m³

0.0005 = 110 \cdot 0.0045

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Polar Moment of Inertia using Polar Modulus Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia using Polar Modulus?

FIRST Step Consider the formula

J = R \cdot Z p

Next Step Substitute values of Variables

∴

J = 110mm \cdot 0.0045m³

Next Step Convert Units

∴

J = 0.11m \cdot 0.0045m³

Next Step Prepare to Evaluate

∴

J = 0.11 \cdot 0.0045

Next Step Evaluate

∴

J = 0.000495m⁴

LAST Step Rounding Answer

∴

J = 0.0005m⁴

Polar Moment of Inertia using Polar 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

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

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

Other Formulas to find Polar Moment of Inertia

Go Polar Moment of Inertia of Solid Shaft

J = \frac{π \cdot d^{4}}{32}

Go Polar Moment of Inertia given Torsional Section Modulus

J = Z p \cdot R

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 using Polar Modulus?

Polar Moment of Inertia using Polar Modulus evaluator uses Polar Moment of Inertia = Radius of Shaft*Polar Modulus to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia using Polar Modulus 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 evaluate Polar Moment of Inertia using Polar Modulus using this online evaluator? To use this online evaluator for Polar Moment of Inertia using Polar Modulus, enter Radius of Shaft (R) & Polar Modulus (Z_p) and hit the calculate button.

FAQs on Polar Moment of Inertia using Polar Modulus

What is the formula to find Polar Moment of Inertia using Polar Modulus?

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

How to calculate Polar Moment of Inertia using Polar Modulus?

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

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

Can the Polar Moment of Inertia using Polar Modulus be negative?

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

Which unit is used to measure Polar Moment of Inertia using Polar Modulus?

Polar Moment of Inertia using Polar 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 using Polar Modulus can be measured.

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Polar Moment of Inertia using Polar Modulus Formula

​GoPolar Moment of Inertia of Solid Shaft Formula

​GoPolar Moment of Inertia given Torsional Section Modulus Formula

Polar Moment of Inertia using Polar Modulus Example

Polar Moment of Inertia using Polar Modulus Solution

Polar Moment of Inertia using Polar Modulus Formula Elements

Other Formulas to find Polar Moment of Inertia

Other formulas in Polar Modulus category

How to Evaluate Polar Moment of Inertia using Polar Modulus?

FAQs on Polar Moment of Inertia using Polar Modulus

Variable Name

GoPolar Moment of Inertia of Solid Shaft Formula

GoPolar Moment of Inertia given Torsional Section Modulus Formula