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Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Formula

GoPolar moment of inertia of shaft given torque transmitted by shaft Formula

GoPolar moment of inertia of shaft Formula

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Polar Moment of Inertia of shaft is the measure of object resistance to torsion. Check FAQs

J shaft = \frac{τ \cdot L}{C \cdot θ}

J_shaft - Polar Moment of Inertia of shaft?τ - Torque Exerted on Wheel?L - Length of Shaft?C - Modulus of Rigidity?θ - Angle of twist?

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Example

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Here is how the Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity equation looks like with Values.

Here is how the Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity equation looks like with Units.

Here is how the Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity equation looks like.

1.4E-10 = \frac{50 \cdot 7000}{84000 \cdot 30}

1.4E-10m⁴ = \frac{50N*m \cdot 7000mm}{84000N/mm² \cdot 30}

1.4E-10 = \frac{50 \cdot 7000}{84000 \cdot 30}

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Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Solution

Follow our step by step solution on how to calculate Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity?

FIRST Step Consider the formula

J shaft = \frac{τ \cdot L}{C \cdot θ}

Next Step Substitute values of Variables

∴

J shaft = \frac{50N*m \cdot 7000mm}{84000N/mm² \cdot 30}

Next Step Convert Units

∴

J shaft = \frac{50N*m \cdot 7m}{8.4E+10Pa \cdot 30}

Next Step Prepare to Evaluate

∴

J shaft = \frac{50 \cdot 7}{8.4E+10 \cdot 30}

Next Step Evaluate

∴

J shaft = 1.38888888888889E-10m⁴

LAST Step Rounding Answer

∴

J shaft = 1.4E-10m⁴

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Formula Elements

Variables

Polar Moment of Inertia of shaft

Polar Moment of Inertia of shaft is the measure of object resistance to torsion.

Symbol: J_shaft

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia of shaft

Torque Exerted on Wheel

Torque Exerted on Wheel is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force. It is characterized by τ.

Symbol: τ

Measurement: TorqueUnit: N*m

Note: Value should be greater than 0.

Formulas to find Torque Exerted on Wheel

Length of Shaft

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

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Modulus of Rigidity

Modulus of Rigidity is the elastic coefficient when a shear force is applied resulting in lateral deformation. It gives us a measure of how rigid a body is.

Symbol: C

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

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: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Angle of twist

Other Formulas to find Polar Moment of Inertia of shaft

Go Polar moment of inertia of shaft given torque transmitted by shaft

J shaft = \frac{τ \cdot R shaft}{𝜏 max}

Go Polar moment of inertia of shaft

J shaft = \frac{π \cdot {d s}^{4}}{32}

Other formulas in Expression for Torque in terms of Polar Moment of Inertia category

Go Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia

C = \frac{τ \cdot L}{θ \cdot J shaft}

Go Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity

L = \frac{C \cdot θ \cdot J shaft}{τ}

Go Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity

θ = \frac{τ \cdot L}{C \cdot J shaft}

Go Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity

τ = \frac{C \cdot θ \cdot J shaft}{L}

How to Evaluate Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity?

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity evaluator uses Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist) to evaluate the Polar Moment of Inertia of shaft, Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity 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 of shaft is denoted by J_shaft symbol.

How to evaluate Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity using this online evaluator? To use this online evaluator for Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity, enter Torque Exerted on Wheel (τ), Length of Shaft (L), Modulus of Rigidity (C) & Angle of twist (θ) and hit the calculate button.

FAQs on Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity

What is the formula to find Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity?

The formula of Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity is expressed as Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist). Here is an example- 1.4E-10 = (50*7)/(84000000000*30).

How to calculate Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity?

With Torque Exerted on Wheel (τ), Length of Shaft (L), Modulus of Rigidity (C) & Angle of twist (θ) we can find Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity using the formula - Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist).

What are the other ways to Calculate Polar Moment of Inertia of shaft?

Here are the different ways to Calculate Polar Moment of Inertia of shaft-

Polar Moment of Inertia of shaft=(Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft
Polar Moment of Inertia of shaft=(pi*Diameter of Shaft^4)/32

Can the Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity be negative?

Yes, the Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity, measured in Second Moment of Area can be negative.

Which unit is used to measure Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity?

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity 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 Shaft given Torque Transmitted and Modulus of Rigidity can be measured.

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Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Formula

​GoPolar moment of inertia of shaft given torque transmitted by shaft Formula

​GoPolar moment of inertia of shaft Formula

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Example

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Solution

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Formula Elements

Other Formulas to find Polar Moment of Inertia of shaft

Other formulas in Expression for Torque in terms of Polar Moment of Inertia category

How to Evaluate Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity?

FAQs on Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity

Variable Name

GoPolar moment of inertia of shaft given torque transmitted by shaft Formula

GoPolar moment of inertia of shaft Formula