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Polar Moment of Inertia of Solid Circular Shaft Formula

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The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape. Check FAQs

J = \frac{π \cdot {d s}^{4}}{32}

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

Polar Moment of Inertia of Solid Circular Shaft Example

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

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

Here is how the Polar Moment of Inertia of Solid Circular 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 Solid Circular Shaft Solution

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

FIRST Step Consider the formula

J = \frac{π \cdot {d s}^{4}}{32}

Next Step Substitute values of Variables

∴

J = \frac{π \cdot {1200mm}^{4}}{32}

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

J = 0.203575203952619m⁴

LAST Step Rounding Answer

∴

J = 0.2036m⁴

Polar Moment of Inertia of Solid Circular Shaft Formula Elements

Variables

Constants

Polar Moment of Inertia

The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia

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

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

Polar Moment of Inertia of Solid Circular Shaft evaluator uses Polar Moment of Inertia = (pi*Diameter of Shaft^4)/32 to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia of Solid Circular Shaft formula is a quantity used to describe resistance to torsional deformation, 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 of Solid Circular Shaft using this online evaluator? To use this online evaluator for Polar Moment of Inertia of Solid Circular Shaft, enter Diameter of Shaft (d_s) and hit the calculate button.

FAQs on Polar Moment of Inertia of Solid Circular Shaft

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

The formula of Polar Moment of Inertia of Solid Circular Shaft is expressed as Polar Moment of Inertia = (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 Solid Circular Shaft?

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

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

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

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

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

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