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Moment of Inertia about Polar Axis 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?

Moment of Inertia about Polar Axis Example

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Here is how the Moment of Inertia about Polar Axis equation looks like with Values.

Here is how the Moment of Inertia about Polar Axis equation looks like with Units.

Here is how the Moment of Inertia about Polar Axis 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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Moment of Inertia about Polar Axis Solution

Follow our step by step solution on how to calculate Moment of Inertia about Polar Axis?

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

Moment of Inertia about Polar Axis 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

Other formulas in Stress and Strain category

Go Elongation Circular Tapered Bar

Δ c = \frac{4 \cdot W load \cdot L bar}{π \cdot D 1 \cdot D 2 \cdot e}

Go Moment of Inertia for Hollow Circular Shaft

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

Go Elongation of Prismatic Bar due to its Own Weight

Δ p = \frac{W load \cdot L bar}{2 \cdot A \cdot e}

Go Deflection of Fixed Beam with Uniformly Distributed Load

d = \frac{W beam \cdot {L beam}^{4}}{384 \cdot e \cdot I}

How to Evaluate Moment of Inertia about Polar Axis?

Moment of Inertia about Polar Axis evaluator uses Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32 to evaluate the Polar Moment of Inertia, The Moment of Inertia about Polar Axis formula is defined as a measure of an object's resistance to changes in its rotation, providing a way to quantify the distribution of mass within an object and its resulting rotational inertia. Polar Moment of Inertia is denoted by J symbol.

How to evaluate Moment of Inertia about Polar Axis using this online evaluator? To use this online evaluator for Moment of Inertia about Polar Axis, enter Diameter of Shaft (d_s) and hit the calculate button.

FAQs on Moment of Inertia about Polar Axis

What is the formula to find Moment of Inertia about Polar Axis?

The formula of Moment of Inertia about Polar Axis 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 Moment of Inertia about Polar Axis?

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

Can the Moment of Inertia about Polar Axis be negative?

Yes, the Moment of Inertia about Polar Axis, measured in Second Moment of Area can be negative.

Which unit is used to measure Moment of Inertia about Polar Axis?

Moment of Inertia about Polar Axis is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Moment of Inertia about Polar Axis can be measured.

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