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

GoPolar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity 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 R shaft}{𝜏 max}

J_shaft - Polar Moment of Inertia of shaft?τ - Torque Exerted on Wheel?R_shaft - Radius of Shaft?𝜏_max - Maximum Shear Stress on Shaft?

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

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Here is how the Polar moment of inertia of shaft given torque transmitted by shaft equation looks like with Values.

Here is how the Polar moment of inertia of shaft given torque transmitted by shaft equation looks like with Units.

Here is how the Polar moment of inertia of shaft given torque transmitted by shaft equation looks like.

0.675 = \frac{50 \cdot 1350}{0.0001}

0.675m⁴ = \frac{50N*m \cdot 1350mm}{0.0001MPa}

0.675 = \frac{50 \cdot 1350}{0.0001}

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

Follow our step by step solution on how to calculate Polar moment of inertia of shaft given torque transmitted by shaft?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

J shaft = \frac{50N*m \cdot 1350mm}{0.0001MPa}

Next Step Convert Units

∴

J shaft = \frac{50N*m \cdot 1.35m}{100Pa}

Next Step Prepare to Evaluate

∴

J shaft = \frac{50 \cdot 1.35}{100}

LAST Step Evaluate

∴

J shaft = 0.675m⁴

Polar moment of inertia of shaft given torque transmitted by shaft 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

Radius of Shaft

Radius of shaft is the distance between the center and the circumference of the shaft.

Symbol: R_shaft

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Radius of Shaft

Maximum Shear Stress on Shaft

Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.

Symbol: 𝜏_max

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Maximum Shear Stress on Shaft

Other Formulas to find Polar Moment of Inertia of shaft

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

J shaft = \frac{τ \cdot L}{C \cdot θ}

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 by shaft?

Polar moment of inertia of shaft given torque transmitted by shaft evaluator uses Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft to evaluate the Polar Moment of Inertia of shaft, Polar moment of inertia of shaft given torque transmitted by shaft 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 by shaft using this online evaluator? To use this online evaluator for Polar moment of inertia of shaft given torque transmitted by shaft, enter Torque Exerted on Wheel (τ), Radius of Shaft (R_shaft) & Maximum Shear Stress on Shaft (𝜏_max) and hit the calculate button.

FAQs on Polar moment of inertia of shaft given torque transmitted by shaft

What is the formula to find Polar moment of inertia of shaft given torque transmitted by shaft?

The formula of Polar moment of inertia of shaft given torque transmitted by shaft is expressed as Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft. Here is an example- 0.675 = (50*1.35)/100.

How to calculate Polar moment of inertia of shaft given torque transmitted by shaft?

With Torque Exerted on Wheel (τ), Radius of Shaft (R_shaft) & Maximum Shear Stress on Shaft (𝜏_max) we can find Polar moment of inertia of shaft given torque transmitted by shaft using the formula - Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft.

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*Length of Shaft)/(Modulus of Rigidity*Angle of twist)
Polar Moment of Inertia of shaft=(pi*Diameter of Shaft^4)/32

Can the Polar moment of inertia of shaft given torque transmitted by shaft be negative?

Yes, the Polar moment of inertia of shaft given torque transmitted by shaft, measured in Second Moment of Area can be negative.

Which unit is used to measure Polar moment of inertia of shaft given torque transmitted by shaft?

Polar moment of inertia of shaft given torque transmitted by 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 shaft given torque transmitted by shaft can be measured.

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

​GoPolar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Formula

​GoPolar moment of inertia of shaft Formula

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

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

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

FAQs on Polar moment of inertia of shaft given torque transmitted by shaft

Variable Name

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

GoPolar moment of inertia of shaft Formula