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Polar moment of inertia Formula

GoPolar Moment of Inertia given twisting moment along with maximum permissible shear stress Formula

GoPolar Moment of Inertia of Hollow Shaft 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 = \frac{T \cdot L shaft}{θ \cdot G Torsion}

J - Polar Moment of Inertia?T - Torque?L_shaft - Length of Shaft?θ - Angle of Twist?G_Torsion - Modulus of Rigidity?

Polar moment of inertia Example

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Here is how the Polar moment of inertia equation looks like with Values.

Here is how the Polar moment of inertia equation looks like with Units.

Here is how the Polar moment of inertia equation looks like.

2.3E-6 = \frac{28 \cdot 4.58}{1.42 \cdot 40}

2.3E-6m⁴ = \frac{28kN*m \cdot 4.58m}{1.42rad \cdot 40GPa}

2.3E-6 = \frac{28 \cdot 4.58}{1.42 \cdot 40}

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Polar moment of inertia Solution

Follow our step by step solution on how to calculate Polar moment of inertia?

FIRST Step Consider the formula

J = \frac{T \cdot L shaft}{θ \cdot G Torsion}

Next Step Substitute values of Variables

∴

J = \frac{28kN*m \cdot 4.58m}{1.42rad \cdot 40GPa}

Next Step Convert Units

∴

J = \frac{28000N*m \cdot 4.58m}{1.42rad \cdot 4E+10Pa}

Next Step Prepare to Evaluate

∴

J = \frac{28000 \cdot 4.58}{1.42 \cdot 4E+10}

Next Step Evaluate

∴

J = 2.25774647887324E-06m⁴

LAST Step Rounding Answer

∴

J = 2.3E-6m⁴

Polar moment of inertia 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

Torque

Torque is a measure of the force that can cause an object to rotate about an axis.

Symbol: T

Measurement: TorqueUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Torque

Length of Shaft

Length of Shaft is the distance between two ends of shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Angle of Twist

Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle of Twist

Modulus of Rigidity

Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

Symbol: G_Torsion

Measurement: PressureUnit: GPa

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Other Formulas to find Polar Moment of Inertia

Go Polar Moment of Inertia given twisting moment along with maximum permissible shear stress

J = T \cdot \frac{R}{τ max}

Go Polar Moment of Inertia of Hollow Shaft

J = \frac{π}{32} \cdot ({d o}^{4} - {d i}^{4})

Other formulas in Torsion category

Go Twisting Moment given Maximum Permissible Shear Stress

T = \frac{J \cdot τ max}{R}

Go Maximum permissible shear stress

τ max = T \cdot \frac{R}{J}

Go Radius with known Maximum permissible shear stress

R = τ max \cdot \frac{J}{T}

Go Maximum permissible shear stress for given Radius and modulus of rigidity

τ max = \frac{G Torsion \cdot (θ) \cdot R}{L shaft}

How to Evaluate Polar moment of inertia?

Polar moment of inertia evaluator uses Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity) to evaluate the Polar Moment of Inertia, The Polar moment of inertia is defined as when Shaft length, Twisting Moment, Modulus of rigidity, and Twist angle the resistance towards torsion. Polar Moment of Inertia is denoted by J symbol.

How to evaluate Polar moment of inertia using this online evaluator? To use this online evaluator for Polar moment of inertia, enter Torque (T), Length of Shaft (L_shaft), Angle of Twist (θ) & Modulus of Rigidity (G_Torsion) and hit the calculate button.

FAQs on Polar moment of inertia

What is the formula to find Polar moment of inertia?

The formula of Polar moment of inertia is expressed as Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity). Here is an example- 2.3E-6 = (28000*4.58)/(1.42*40000000000).

How to calculate Polar moment of inertia?

With Torque (T), Length of Shaft (L_shaft), Angle of Twist (θ) & Modulus of Rigidity (G_Torsion) we can find Polar moment of inertia using the formula - Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity).

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=Torque*Radius of Shaft/Maximum Shear Stress
Polar Moment of Inertia=pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)

Can the Polar moment of inertia be negative?

No, the Polar moment of inertia, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar moment of inertia?

Polar moment of inertia 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 can be measured.

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Polar moment of inertia Formula

​GoPolar Moment of Inertia given twisting moment along with maximum permissible shear stress Formula

​GoPolar Moment of Inertia of Hollow Shaft Formula

Polar moment of inertia Example

Polar moment of inertia Solution

Polar moment of inertia Formula Elements

Other Formulas to find Polar Moment of Inertia

Other formulas in Torsion category

How to Evaluate Polar moment of inertia?

FAQs on Polar moment of inertia

Variable Name

GoPolar Moment of Inertia given twisting moment along with maximum permissible shear stress Formula

GoPolar Moment of Inertia of Hollow Shaft Formula