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Twist angle given Shaft length and modulus of rigidity Formula

GoTwist angle given maximum permissible shear stress Formula

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Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end. Check FAQs

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

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

Twist angle given Shaft length and modulus of rigidity Example

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Here is how the Twist angle given Shaft length and modulus of rigidity equation looks like with Values.

Here is how the Twist angle given Shaft length and modulus of rigidity equation looks like with Units.

Here is how the Twist angle given Shaft length and modulus of rigidity equation looks like.

0.0008 = \frac{28 \cdot 4.58}{0.0041 \cdot 40}

0.0008rad = \frac{28kN*m \cdot 4.58m}{0.0041m⁴ \cdot 40GPa}

0.0008 = \frac{28 \cdot 4.58}{0.0041 \cdot 40}

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Twist angle given Shaft length and modulus of rigidity Solution

Follow our step by step solution on how to calculate Twist angle given Shaft length and modulus of rigidity?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ = \frac{28kN*m \cdot 4.58m}{0.0041m⁴ \cdot 40GPa}

Next Step Convert Units

∴

θ = \frac{28000N*m \cdot 4.58m}{0.0041m⁴ \cdot 4E+10Pa}

Next Step Prepare to Evaluate

∴

θ = \frac{28000 \cdot 4.58}{0.0041 \cdot 4E+10}

Next Step Evaluate

∴

θ = 0.000781951219512195rad

LAST Step Rounding Answer

∴

θ = 0.0008rad

Twist angle given Shaft length and modulus of rigidity Formula Elements

Variables

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

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

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

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

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

Other Formulas to find Angle of Twist

Go Twist angle given maximum permissible shear stress

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

Other formulas in Torsion category

Go Twisting Moment given Maximum Permissible Shear Stress

T = \frac{J \cdot τ max}{R}

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}

How to Evaluate Twist angle given Shaft length and modulus of rigidity?

Twist angle given Shaft length and modulus of rigidity evaluator uses Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity) to evaluate the Angle of Twist, The Twist angle given Shaft length and modulus of rigidity along with Polar Moment of Inertia and Twisting Moment is defined as the angle of rotation of any plane taken along the axis of the shaft. Angle of Twist is denoted by θ symbol.

How to evaluate Twist angle given Shaft length and modulus of rigidity using this online evaluator? To use this online evaluator for Twist angle given Shaft length and modulus of rigidity, enter Torque (T), Length of Shaft (L_shaft), Polar Moment of Inertia (J) & Modulus of Rigidity (G_Torsion) and hit the calculate button.

FAQs on Twist angle given Shaft length and modulus of rigidity

What is the formula to find Twist angle given Shaft length and modulus of rigidity?

The formula of Twist angle given Shaft length and modulus of rigidity is expressed as Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity). Here is an example- 0.000782 = (28000*4.58)/(0.0041*40000000000).

How to calculate Twist angle given Shaft length and modulus of rigidity?

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

What are the other ways to Calculate Angle of Twist?

Here are the different ways to Calculate Angle of Twist-

Angle of Twist=(Maximum Shear Stress*Length of Shaft)/(Radius of Shaft*Modulus of Rigidity)

Can the Twist angle given Shaft length and modulus of rigidity be negative?

Yes, the Twist angle given Shaft length and modulus of rigidity, measured in Angle can be negative.

Which unit is used to measure Twist angle given Shaft length and modulus of rigidity?

Twist angle given Shaft length and modulus of rigidity is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Twist angle given Shaft length and modulus of rigidity can be measured.

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Twist angle given Shaft length and modulus of rigidity Formula

​GoTwist angle given maximum permissible shear stress Formula

Twist angle given Shaft length and modulus of rigidity Example

Twist angle given Shaft length and modulus of rigidity Solution

Twist angle given Shaft length and modulus of rigidity Formula Elements

Other Formulas to find Angle of Twist

Other formulas in Torsion category

How to Evaluate Twist angle given Shaft length and modulus of rigidity?

FAQs on Twist angle given Shaft length and modulus of rigidity

Variable Name

GoTwist angle given maximum permissible shear stress Formula