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Polar Moment of Inertia of Hollow Circular 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 outer}^{4} - {d inner}^{4})}{32}

J_shaft - Polar Moment of Inertia of shaft?d_outer - Outer Diameter of Shaft?d_inner - Inner Diameter of Shaft?π - Archimedes' constant?

Polar Moment of Inertia of Hollow Circular Shaft Example

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Here is how the Polar Moment of Inertia of Hollow Circular Shaft equation looks like with Values.

Here is how the Polar Moment of Inertia of Hollow Circular Shaft equation looks like with Units.

Here is how the Polar Moment of Inertia of Hollow Circular Shaft equation looks like.

25.0346 = \frac{3.1416 \cdot (4000^{4} - 1000^{4})}{32}

25.0346m⁴ = \frac{3.1416 \cdot ({4000mm}^{4} - {1000mm}^{4})}{32}

25.0346 = \frac{3.1416 \cdot (4000^{4} - 1000^{4})}{32}

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Polar Moment of Inertia of Hollow Circular Shaft Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia of Hollow Circular Shaft?

FIRST Step Consider the formula

J shaft = \frac{π \cdot ({d outer}^{4} - {d inner}^{4})}{32}

Next Step Substitute values of Variables

∴

J shaft = \frac{π \cdot ({4000mm}^{4} - {1000mm}^{4})}{32}

Next Step Substitute values of Constants

∴

J shaft = \frac{3.1416 \cdot ({4000mm}^{4} - {1000mm}^{4})}{32}

Next Step Convert Units

∴

J shaft = \frac{3.1416 \cdot ({4m}^{4} - {1m}^{4})}{32}

Next Step Prepare to Evaluate

∴

J shaft = \frac{3.1416 \cdot (4^{4} - 1^{4})}{32}

Next Step Evaluate

∴

J shaft = 25.0345664582937m⁴

LAST Step Rounding Answer

∴

J shaft = 25.0346m⁴

Polar Moment of Inertia of Hollow Circular 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

Outer Diameter of Shaft

Outer Diameter of Shaft is defined as the length of the longest chord of the surface of the hollow circular shaft.

Symbol: d_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Diameter of Shaft

Inner Diameter of Shaft

The Inner Diameter of Shaft is defined as the length of the longest chord inside the hollow shaft.

Symbol: d_inner

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Inner 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 in Design of Hollow Shaft category

Go Ratio of Inner Diameter to Outer Diameter

C = \frac{d i}{d o}

Go Inner Diameter of Hollow Shaft given Ratio of Diameters

d i = C \cdot d o

Go Outer Diameter given Ratio of Diameters

d o = \frac{d i}{C}

Go Tensile Stress in Hollow Shaft when Subjected to Axial Force

σ tp = \frac{P ax hollow}{\frac{π}{4} \cdot ({d o}^{2} - {d i}^{2})}

How to Evaluate Polar Moment of Inertia of Hollow Circular Shaft?

Polar Moment of Inertia of Hollow Circular Shaft evaluator uses Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32 to evaluate the Polar Moment of Inertia of shaft, Polar Moment of Inertia of Hollow Circular Shaft formula is defined as a measure of the shaft's resistance to torsional deformation, which is essential in designing hollow circular shafts to withstand twisting forces and ensure structural integrity in mechanical systems. Polar Moment of Inertia of shaft is denoted by J_shaft symbol.

How to evaluate Polar Moment of Inertia of Hollow Circular Shaft using this online evaluator? To use this online evaluator for Polar Moment of Inertia of Hollow Circular Shaft, enter Outer Diameter of Shaft (d_outer) & Inner Diameter of Shaft (d_inner) and hit the calculate button.

FAQs on Polar Moment of Inertia of Hollow Circular Shaft

What is the formula to find Polar Moment of Inertia of Hollow Circular Shaft?

The formula of Polar Moment of Inertia of Hollow Circular Shaft is expressed as Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32. Here is an example- 25.03457 = (pi*(4^(4)-1^(4)))/32.

How to calculate Polar Moment of Inertia of Hollow Circular Shaft?

With Outer Diameter of Shaft (d_outer) & Inner Diameter of Shaft (d_inner) we can find Polar Moment of Inertia of Hollow Circular Shaft using the formula - Polar Moment of Inertia of shaft = (pi*(Outer Diameter of Shaft^(4)-Inner Diameter of Shaft^(4)))/32. This formula also uses Archimedes' constant .

Can the Polar Moment of Inertia of Hollow Circular Shaft be negative?

Yes, the Polar Moment of Inertia of Hollow Circular Shaft, measured in Second Moment of Area can be negative.

Which unit is used to measure Polar Moment of Inertia of Hollow Circular Shaft?

Polar Moment of Inertia of Hollow Circular 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 Hollow Circular Shaft can be measured.

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Polar Moment of Inertia of Hollow Circular Shaft Formula

Polar Moment of Inertia of Hollow Circular Shaft Example

Polar Moment of Inertia of Hollow Circular Shaft Solution

Polar Moment of Inertia of Hollow Circular Shaft Formula Elements

Other formulas in Design of Hollow Shaft category

How to Evaluate Polar Moment of Inertia of Hollow Circular Shaft?

FAQs on Polar Moment of Inertia of Hollow Circular Shaft

Variable Name