FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Polar Moment of Inertia of Solid Shaft Formula

GoPolar Moment of Inertia using Polar Modulus Formula

GoPolar Moment of Inertia given Torsional Section Modulus Formula

Fx Copy

LaTeX Copy

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 = \frac{π \cdot d^{4}}{32}

J - Polar Moment of Inertia?d - Dia of Shaft?π - Archimedes' constant?

Polar Moment of Inertia of Solid Shaft Example

With values

With units

Only example

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

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

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

0.0006 = \frac{3.1416 \cdot {0.284}^{4}}{32}

0.0006m⁴ = \frac{3.1416 \cdot {0.284m}^{4}}{32}

0.0006 = \frac{3.1416 \cdot {0.284}^{4}}{32}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Strength of Materials » fx Polar Moment of Inertia of Solid Shaft

Polar Moment of Inertia of Solid Shaft Solution

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

FIRST Step Consider the formula

J = \frac{π \cdot d^{4}}{32}

Next Step Substitute values of Variables

∴

J = \frac{π \cdot {0.284m}^{4}}{32}

Next Step Substitute values of Constants

∴

J = \frac{3.1416 \cdot {0.284m}^{4}}{32}

Next Step Prepare to Evaluate

∴

J = \frac{3.1416 \cdot {0.284}^{4}}{32}

Next Step Evaluate

∴

J = 0.000638665202759738m⁴

LAST Step Rounding Answer

∴

J = 0.0006m⁴

Polar Moment of Inertia of Solid Shaft Formula Elements

Variables

Constants

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

Dia of Shaft

The Dia 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

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Dia 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 to find Polar Moment of Inertia

Go Polar Moment of Inertia using Polar Modulus

J = R \cdot Z p

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 of Solid Shaft?

Polar Moment of Inertia of Solid Shaft evaluator uses Polar Moment of Inertia = (pi*Dia of Shaft^4)/32 to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia of Solid Shaft 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 of Solid Shaft using this online evaluator? To use this online evaluator for Polar Moment of Inertia of Solid Shaft, enter Dia of Shaft (d) and hit the calculate button.

FAQs on Polar Moment of Inertia of Solid Shaft

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

The formula of Polar Moment of Inertia of Solid Shaft is expressed as Polar Moment of Inertia = (pi*Dia of Shaft^4)/32. Here is an example- 0.000639 = (pi*0.284^4)/32.

How to calculate Polar Moment of Inertia of Solid Shaft?

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

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=Polar Modulus*Radius of Shaft

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

No, the Polar Moment of Inertia of Solid Shaft, measured in Second Moment of Area cannot be negative.

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

Polar Moment of Inertia of Solid 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 Shaft can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit