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

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

L = \frac{C \cdot θ \cdot J shaft}{τ}

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

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

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

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

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

5E+14 = \frac{84000 \cdot 30 \cdot 10}{50}

5E+14mm = \frac{84000N/mm² \cdot 30 \cdot 10m⁴}{50N*m}

5E+14 = \frac{84000 \cdot 30 \cdot 10}{50}

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

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

FIRST Step Consider the formula

L = \frac{C \cdot θ \cdot J shaft}{τ}

Next Step Substitute values of Variables

∴

L = \frac{84000N/mm² \cdot 30 \cdot 10m⁴}{50N*m}

Next Step Convert Units

∴

L = \frac{8.4E+10Pa \cdot 30 \cdot 10m⁴}{50N*m}

Next Step Prepare to Evaluate

∴

L = \frac{8.4E+10 \cdot 30 \cdot 10}{50}

Next Step Evaluate

∴

L = 504000000000m

Next Step Convert to Output's Unit

∴

L = 504000000000000mm

LAST Step Rounding Answer

∴

L = 5E+14mm

Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity Formula Elements

Variables

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

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

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

J shaft = \frac{τ \cdot L}{C \cdot θ}

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

Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity evaluator uses Length of Shaft = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel to evaluate the Length of Shaft, Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity is defined as the measurement or extent of something from end to end. Length of Shaft is denoted by L symbol.

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

FAQs on Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity

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

The formula of Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity is expressed as Length of Shaft = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel. Here is an example- 5E+17 = (84000000000*30*10)/50.

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

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

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

No, the Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity, measured in Length cannot be negative.

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

Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity can be measured.

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

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

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

Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity Formula Elements

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

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

FAQs on Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity

Variable Name