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

GoPolar moment of inertia 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 = T \cdot \frac{R}{τ max}

J - Polar Moment of Inertia?T - Torque?R - Radius of Shaft?τ_max - Maximum Shear Stress?

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

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Here is how the Polar Moment of Inertia given twisting moment along with maximum permissible shear stress equation looks like with Values.

Here is how the Polar Moment of Inertia given twisting moment along with maximum permissible shear stress equation looks like with Units.

Here is how the Polar Moment of Inertia given twisting moment along with maximum permissible shear stress equation looks like.

7.3E-5 = 28 \cdot \frac{110}{42}

7.3E-5m⁴ = 28kN*m \cdot \frac{110mm}{42MPa}

7.3E-5 = 28 \cdot \frac{110}{42}

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

Follow our step by step solution on how to calculate Polar Moment of Inertia given twisting moment along with maximum permissible shear stress?

FIRST Step Consider the formula

J = T \cdot \frac{R}{τ max}

Next Step Substitute values of Variables

∴

J = 28kN*m \cdot \frac{110mm}{42MPa}

Next Step Convert Units

∴

J = 28000N*m \cdot \frac{0.11m}{4.2E+7Pa}

Next Step Prepare to Evaluate

∴

J = 28000 \cdot \frac{0.11}{4.2E+7}

Next Step Evaluate

∴

J = 7.33333333333333E-05m⁴

LAST Step Rounding Answer

∴

J = 7.3E-5m⁴

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

Radius of Shaft

The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Shaft

Maximum Shear Stress

Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

Symbol: τ_max

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Shear Stress

Other Formulas to find Polar Moment of Inertia

Go Polar moment of inertia

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

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 given twisting moment along with maximum permissible shear stress?

Polar Moment of Inertia given twisting moment along with maximum permissible shear stress evaluator uses Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress to evaluate the Polar Moment of Inertia, The Polar Moment of Inertia given twisting moment along with maximum permissible shear stress is defined as the resistance towards torsion. Polar Moment of Inertia is denoted by J symbol.

How to evaluate Polar Moment of Inertia given twisting moment along with maximum permissible shear stress using this online evaluator? To use this online evaluator for Polar Moment of Inertia given twisting moment along with maximum permissible shear stress, enter Torque (T), Radius of Shaft (R) & Maximum Shear Stress (τ_max) and hit the calculate button.

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

What is the formula to find Polar Moment of Inertia given twisting moment along with maximum permissible shear stress?

The formula of Polar Moment of Inertia given twisting moment along with maximum permissible shear stress is expressed as Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress. Here is an example- 7.3E-5 = 28000*0.11/42000000.

How to calculate Polar Moment of Inertia given twisting moment along with maximum permissible shear stress?

With Torque (T), Radius of Shaft (R) & Maximum Shear Stress (τ_max) we can find Polar Moment of Inertia given twisting moment along with maximum permissible shear stress using the formula - Polar Moment of Inertia = Torque*Radius of Shaft/Maximum Shear Stress.

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*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)
Polar Moment of Inertia=pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)

Can the Polar Moment of Inertia given twisting moment along with maximum permissible shear stress be negative?

No, the Polar Moment of Inertia given twisting moment along with maximum permissible shear stress, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar Moment of Inertia given twisting moment along with maximum permissible shear stress?

Polar Moment of Inertia given twisting moment along with maximum permissible shear stress 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 given twisting moment along with maximum permissible shear stress can be measured.

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

​GoPolar moment of inertia Formula

​GoPolar Moment of Inertia of Hollow Shaft Formula

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

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

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

Other Formulas to find Polar Moment of Inertia

Other formulas in Torsion category

How to Evaluate Polar Moment of Inertia given twisting moment along with maximum permissible shear stress?

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

Variable Name

GoPolar moment of inertia Formula

GoPolar Moment of Inertia of Hollow Shaft Formula