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

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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. Check FAQs

C = \frac{τ \cdot L}{θ \cdot J shaft}

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

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

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

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

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

1.2E-6 = \frac{50 \cdot 7000}{30 \cdot 10}

1.2E-6N/mm² = \frac{50N*m \cdot 7000mm}{30 \cdot 10m⁴}

1.2E-6 = \frac{50 \cdot 7000}{30 \cdot 10}

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

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

FIRST Step Consider the formula

C = \frac{τ \cdot L}{θ \cdot J shaft}

Next Step Substitute values of Variables

∴

C = \frac{50N*m \cdot 7000mm}{30 \cdot 10m⁴}

Next Step Convert Units

∴

C = \frac{50N*m \cdot 7m}{30 \cdot 10m⁴}

Next Step Prepare to Evaluate

∴

C = \frac{50 \cdot 7}{30 \cdot 10}

Next Step Evaluate

∴

C = 1.16666666666667Pa

Next Step Convert to Output's Unit

∴

C = 1.16666666666667E-06N/mm²

LAST Step Rounding Answer

∴

C = 1.2E-6N/mm²

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

Variables

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

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

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

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

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

J shaft = \frac{τ \cdot L}{C \cdot θ}

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

Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia evaluator uses Modulus of Rigidity = (Torque Exerted on Wheel*Length of Shaft)/(Angle of twist*Polar Moment of Inertia of shaft) to evaluate the Modulus of Rigidity, Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia is defined as the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. Modulus of Rigidity is denoted by C symbol.

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

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

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

The formula of Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia is expressed as Modulus of Rigidity = (Torque Exerted on Wheel*Length of Shaft)/(Angle of twist*Polar Moment of Inertia of shaft). Here is an example- 1.2E-12 = (50*7)/(30*10).

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

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

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

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

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

Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia can be measured.

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

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

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

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

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

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

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

Variable Name