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Polar moment of inertia of shaft given shear stress and torsional moment Formula

GoPolar moment of inertia of hollow circular cross-section Formula

GoPolar moment of inertia of circular cross section Formula

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Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion. Check FAQs

J = τ \cdot \frac{r}{𝜏}

J - Polar moment of inertia for circular section?τ - Torsional moment on shaft?r - Radial Distance from Axis of Rotation?𝜏 - Torsional shear stress in twisted shaft?

Polar moment of inertia of shaft given shear stress and torsional moment Example

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Here is how the Polar moment of inertia of shaft given shear stress and torsional moment equation looks like with Values.

Here is how the Polar moment of inertia of shaft given shear stress and torsional moment equation looks like with Units.

Here is how the Polar moment of inertia of shaft given shear stress and torsional moment equation looks like.

36428.5714 = 51000 \cdot \frac{25}{35}

36428.5714mm⁴ = 51000N*mm \cdot \frac{25mm}{35N/mm²}

36428.5714 = 51000 \cdot \frac{25}{35}

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Polar moment of inertia of shaft given shear stress and torsional moment Solution

Follow our step by step solution on how to calculate Polar moment of inertia of shaft given shear stress and torsional moment?

FIRST Step Consider the formula

J = τ \cdot \frac{r}{𝜏}

Next Step Substitute values of Variables

∴

J = 51000N*mm \cdot \frac{25mm}{35N/mm²}

Next Step Convert Units

∴

J = 51N*m \cdot \frac{0.025m}{3.5E+7Pa}

Next Step Prepare to Evaluate

∴

J = 51 \cdot \frac{0.025}{3.5E+7}

Next Step Evaluate

∴

J = 3.64285714285714E-08m⁴

Next Step Convert to Output's Unit

∴

J = 36428.5714285714mm⁴

LAST Step Rounding Answer

∴

J = 36428.5714mm⁴

Polar moment of inertia of shaft given shear stress and torsional moment Formula Elements

Variables

Polar moment of inertia for circular section

Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion.

Symbol: J

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Polar moment of inertia for circular section

Torsional moment on shaft

Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.

Symbol: τ

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Torsional moment on shaft

Radial Distance from Axis of Rotation

Radial Distance from Axis of Rotation is taken as the distance between the projections onto the two planes.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radial Distance from Axis of Rotation

Torsional shear stress in twisted shaft

Torsional shear stress in twisted shaft or Torsional stress is the shear stress produced in the shaft due to the twisting.

Symbol: 𝜏

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Torsional shear stress in twisted shaft

Other Formulas to find Polar moment of inertia for circular section

Go Polar moment of inertia of hollow circular cross-section

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

Go Polar moment of inertia of circular cross section

J = π \cdot \frac{{d c}^{4}}{32}

Other formulas in Design of Shaft for Torsional Moment category

Go Torsional shear stress in shaft due to torsional moment

𝜏 = τ \cdot \frac{r}{J}

Go Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia

θ = \frac{τ \cdot l}{J \cdot C}

Go Angle of twist of solid cylindrical rod in degrees

𝜽 d = (584 \cdot τ \cdot \frac{l}{C \cdot ({d c}^{4})}) \cdot (\frac{π}{180})

Go Angle of twist of hollow cylindrical rod in degrees

𝜽 d = (584 \cdot τ \cdot \frac{l}{C \cdot (({d ho}^{4}) - ({d hi}^{4}))}) \cdot (\frac{π}{180})

How to Evaluate Polar moment of inertia of shaft given shear stress and torsional moment?

Polar moment of inertia of shaft given shear stress and torsional moment evaluator uses Polar moment of inertia for circular section = Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft to evaluate the Polar moment of inertia for circular section, Polar moment of inertia of shaft given shear stress and torsional moment formula basically describes the cylindrical object's (including its segments) resistance to torsional deformation when torque is applied in a plane that is parallel to the cross-section area or in a plane that is perpendicular to the object's central axis. Polar moment of inertia for circular section is denoted by J symbol.

How to evaluate Polar moment of inertia of shaft given shear stress and torsional moment using this online evaluator? To use this online evaluator for Polar moment of inertia of shaft given shear stress and torsional moment, enter Torsional moment on shaft (τ), Radial Distance from Axis of Rotation (r) & Torsional shear stress in twisted shaft (𝜏) and hit the calculate button.

FAQs on Polar moment of inertia of shaft given shear stress and torsional moment

What is the formula to find Polar moment of inertia of shaft given shear stress and torsional moment?

The formula of Polar moment of inertia of shaft given shear stress and torsional moment is expressed as Polar moment of inertia for circular section = Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft. Here is an example- 3.6E+16 = 51*0.025/35000000.

How to calculate Polar moment of inertia of shaft given shear stress and torsional moment?

With Torsional moment on shaft (τ), Radial Distance from Axis of Rotation (r) & Torsional shear stress in twisted shaft (𝜏) we can find Polar moment of inertia of shaft given shear stress and torsional moment using the formula - Polar moment of inertia for circular section = Torsional moment on shaft*Radial Distance from Axis of Rotation/Torsional shear stress in twisted shaft.

What are the other ways to Calculate Polar moment of inertia for circular section?

Here are the different ways to Calculate Polar moment of inertia for circular section-

Polar moment of inertia for circular section=pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32
Polar moment of inertia for circular section=pi*(Diameter of circular section of shaft^4)/32

Can the Polar moment of inertia of shaft given shear stress and torsional moment be negative?

No, the Polar moment of inertia of shaft given shear stress and torsional moment, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Polar moment of inertia of shaft given shear stress and torsional moment?

Polar moment of inertia of shaft given shear stress and torsional moment is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Polar moment of inertia of shaft given shear stress and torsional moment can be measured.

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Polar moment of inertia of shaft given shear stress and torsional moment Formula

​GoPolar moment of inertia of hollow circular cross-section Formula

​GoPolar moment of inertia of circular cross section Formula

Polar moment of inertia of shaft given shear stress and torsional moment Example

Polar moment of inertia of shaft given shear stress and torsional moment Solution

Polar moment of inertia of shaft given shear stress and torsional moment Formula Elements

Other Formulas to find Polar moment of inertia for circular section

Other formulas in Design of Shaft for Torsional Moment category

How to Evaluate Polar moment of inertia of shaft given shear stress and torsional moment?

FAQs on Polar moment of inertia of shaft given shear stress and torsional moment

Variable Name

GoPolar moment of inertia of hollow circular cross-section Formula

GoPolar moment of inertia of circular cross section Formula