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Twisting Moment given Polar MOI and Twist Angle Formula

GoTwisting Moment given Maximum Permissible Shear Stress Formula

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Torque is a measure of the force that can cause an object to rotate about an axis. Check FAQs

T = \frac{G Torsion \cdot θ \cdot J}{L shaft}

T - Torque?G_Torsion - Modulus of Rigidity?θ - Angle of Twist?J - Polar Moment of Inertia?L_shaft - Length of Shaft?

Twisting Moment given Polar MOI and Twist Angle Example

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Here is how the Twisting Moment given Polar MOI and Twist Angle equation looks like with Values.

Here is how the Twisting Moment given Polar MOI and Twist Angle equation looks like with Units.

Here is how the Twisting Moment given Polar MOI and Twist Angle equation looks like.

50847.1616 = \frac{40 \cdot 1.42 \cdot 0.0041}{4.58}

50847.1616kN*m = \frac{40GPa \cdot 1.42rad \cdot 0.0041m⁴}{4.58m}

50847.1616 = \frac{40 \cdot 1.42 \cdot 0.0041}{4.58}

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Twisting Moment given Polar MOI and Twist Angle Solution

Follow our step by step solution on how to calculate Twisting Moment given Polar MOI and Twist Angle?

FIRST Step Consider the formula

T = \frac{G Torsion \cdot θ \cdot J}{L shaft}

Next Step Substitute values of Variables

∴

T = \frac{40GPa \cdot 1.42rad \cdot 0.0041m⁴}{4.58m}

Next Step Convert Units

∴

T = \frac{4E+10Pa \cdot 1.42rad \cdot 0.0041m⁴}{4.58m}

Next Step Prepare to Evaluate

∴

T = \frac{4E+10 \cdot 1.42 \cdot 0.0041}{4.58}

Next Step Evaluate

∴

T = 50847161.5720524N*m

Next Step Convert to Output's Unit

∴

T = 50847.1615720524kN*m

LAST Step Rounding Answer

∴

T = 50847.1616kN*m

Twisting Moment given Polar MOI and Twist Angle Formula Elements

Variables

Torque

Torque is a measure of the force that can cause an object to rotate about an axis.

Symbol: T

Measurement: TorqueUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Torque

Modulus of Rigidity

Modulus of Rigidity is the measure of the rigidity of the body, given by the ratio of shear stress to shear strain. It is often denoted by G.

Symbol: G_Torsion

Measurement: PressureUnit: GPa

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: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle of Twist

Polar Moment of Inertia

Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Length of Shaft

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

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Other Formulas to find Torque

Go Twisting Moment given Maximum Permissible Shear Stress

T = \frac{J \cdot τ max}{R}

Other formulas in Torsion category

Go Maximum permissible shear stress

τ max = T \cdot \frac{R}{J}

Go Radius with known Maximum permissible shear stress

R = τ max \cdot \frac{J}{T}

Go Maximum permissible shear stress for given Radius and modulus of rigidity

τ max = \frac{G Torsion \cdot (θ) \cdot R}{L shaft}

Go Modulus of rigidity given maximum permissible shear stress

G Torsion = \frac{τ max \cdot L shaft}{θ \cdot R}

How to Evaluate Twisting Moment given Polar MOI and Twist Angle?

Twisting Moment given Polar MOI and Twist Angle evaluator uses Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft to evaluate the Torque, The Twisting Moment given Polar MOI and Twist Angle formula is defined as the moment given to the shaft to twist it. Torque is denoted by T symbol.

How to evaluate Twisting Moment given Polar MOI and Twist Angle using this online evaluator? To use this online evaluator for Twisting Moment given Polar MOI and Twist Angle, enter Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Polar Moment of Inertia (J) & Length of Shaft (L_shaft) and hit the calculate button.

FAQs on Twisting Moment given Polar MOI and Twist Angle

What is the formula to find Twisting Moment given Polar MOI and Twist Angle?

The formula of Twisting Moment given Polar MOI and Twist Angle is expressed as Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft. Here is an example- 50.84716 = (40000000000*1.42*0.0041)/4.58.

How to calculate Twisting Moment given Polar MOI and Twist Angle?

With Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Polar Moment of Inertia (J) & Length of Shaft (L_shaft) we can find Twisting Moment given Polar MOI and Twist Angle using the formula - Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft.

What are the other ways to Calculate Torque?

Here are the different ways to Calculate Torque-

Torque=(Polar Moment of Inertia*Maximum Shear Stress)/Radius of Shaft

Can the Twisting Moment given Polar MOI and Twist Angle be negative?

Yes, the Twisting Moment given Polar MOI and Twist Angle, measured in Torque can be negative.

Which unit is used to measure Twisting Moment given Polar MOI and Twist Angle?

Twisting Moment given Polar MOI and Twist Angle is usually measured using the Kilonewton Meter[kN*m] for Torque. Newton Meter[kN*m], Newton Centimeter[kN*m], Newton Millimeter[kN*m] are the few other units in which Twisting Moment given Polar MOI and Twist Angle can be measured.

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Twisting Moment given Polar MOI and Twist Angle Formula

​GoTwisting Moment given Maximum Permissible Shear Stress Formula

Twisting Moment given Polar MOI and Twist Angle Example

Twisting Moment given Polar MOI and Twist Angle Solution

Twisting Moment given Polar MOI and Twist Angle Formula Elements

Other Formulas to find Torque

Other formulas in Torsion category

How to Evaluate Twisting Moment given Polar MOI and Twist Angle?

FAQs on Twisting Moment given Polar MOI and Twist Angle

Variable Name

GoTwisting Moment given Maximum Permissible Shear Stress Formula