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Total Angle of Twist for Shaft 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{32 \cdot τ \cdot L \cdot (\frac{1}{{D 1}^{3}} - \frac{1}{{D 2}^{3}})}{π \cdot G \cdot (D 2 - D 1)}

θ - Angle of twist?τ - Torque Exerted on Wheel?L - Length of Shaft?D₁ - Diameter of shaft at left end?D₂ - Diameter of shaft at right end?G - Modulus of rigidity of Shaft?π - Archimedes' constant?

Total Angle of Twist for Shaft Example

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Here is how the Total Angle of Twist for Shaft equation looks like with Values.

Here is how the Total Angle of Twist for Shaft equation looks like with Units.

Here is how the Total Angle of Twist for Shaft equation looks like.

1.294 = \frac{32 \cdot 50 \cdot 7000 \cdot (\frac{1}{3000^{3}} - \frac{1}{5000^{3}})}{3.1416 \cdot 4E-5 \cdot (5000 - 3000)}

1.294 = \frac{32 \cdot 50N*m \cdot 7000mm \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}{3.1416 \cdot 4E-5MPa \cdot (5000mm - 3000mm)}

1.294 = \frac{32 \cdot 50 \cdot 7000 \cdot (\frac{1}{3000^{3}} - \frac{1}{5000^{3}})}{3.1416 \cdot 4E-5 \cdot (5000 - 3000)}

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Total Angle of Twist for Shaft Solution

Follow our step by step solution on how to calculate Total Angle of Twist for Shaft?

FIRST Step Consider the formula

θ = \frac{32 \cdot τ \cdot L \cdot (\frac{1}{{D 1}^{3}} - \frac{1}{{D 2}^{3}})}{π \cdot G \cdot (D 2 - D 1)}

Next Step Substitute values of Variables

∴

θ = \frac{32 \cdot 50N*m \cdot 7000mm \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}{π \cdot 4E-5MPa \cdot (5000mm - 3000mm)}

Next Step Substitute values of Constants

∴

θ = \frac{32 \cdot 50N*m \cdot 7000mm \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}{3.1416 \cdot 4E-5MPa \cdot (5000mm - 3000mm)}

Next Step Convert Units

∴

θ = \frac{32 \cdot 50N*m \cdot 7m \cdot (\frac{1}{{3m}^{3}} - \frac{1}{{5m}^{3}})}{3.1416 \cdot 40Pa \cdot (5m - 3m)}

Next Step Prepare to Evaluate

∴

θ = \frac{32 \cdot 50 \cdot 7 \cdot (\frac{1}{3^{3}} - \frac{1}{5^{3}})}{3.1416 \cdot 40 \cdot (5 - 3)}

Next Step Evaluate

∴

θ = 1.29398863361233

LAST Step Rounding Answer

∴

θ = 1.294

Total Angle of Twist for Shaft Formula Elements

Variables

Constants

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

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

Diameter of shaft at left end

Diameter of shaft at left end is the shorter side diameter of tapering shaft.

Symbol: D₁

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of shaft at left end

Diameter of shaft at right end

Diameter of shaft at right end is the longer side diameter of tapering shaft.

Symbol: D₂

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of shaft at right end

Modulus of rigidity of Shaft

Modulus of rigidity of Shaft 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: G

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of rigidity of Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Torsion of Tapering Shafts category

Go Torque on Tapering Shaft

τ = \frac{𝜏 \cdot π \cdot d s}{16}

Go Shear Stress on Left Surface of Shaft

𝜏 = \frac{16 \cdot τ}{π \cdot d s}

Go Diameter of Shaft at Left End

d s = \frac{16 \cdot τ}{𝜏 \cdot π}

Go Torque on Shaft given Total Angle of Twist for Shaft

τ = \frac{θ \cdot π \cdot G \cdot (D 2 - D 1)}{32 \cdot L \cdot (\frac{1}{{D 1}^{3}} - \frac{1}{{D 2}^{3}})}

How to Evaluate Total Angle of Twist for Shaft?

Total Angle of Twist for Shaft evaluator uses Angle of twist = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end)) to evaluate the Angle of twist, Total angle of twist for shaft is the angle through which the fixed end of a shaft rotates with respect to the free end. Angle of twist is denoted by θ symbol.

How to evaluate Total Angle of Twist for Shaft using this online evaluator? To use this online evaluator for Total Angle of Twist for Shaft, enter Torque Exerted on Wheel (τ), Length of Shaft (L), Diameter of shaft at left end (D₁), Diameter of shaft at right end (D₂) & Modulus of rigidity of Shaft (G) and hit the calculate button.

FAQs on Total Angle of Twist for Shaft

What is the formula to find Total Angle of Twist for Shaft?

The formula of Total Angle of Twist for Shaft is expressed as Angle of twist = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end)). Here is an example- 1.293989 = (32*50*7*(1/(3^3)-1/(5^3)))/(pi*40*(5-3)).

How to calculate Total Angle of Twist for Shaft?

With Torque Exerted on Wheel (τ), Length of Shaft (L), Diameter of shaft at left end (D₁), Diameter of shaft at right end (D₂) & Modulus of rigidity of Shaft (G) we can find Total Angle of Twist for Shaft using the formula - Angle of twist = (32*Torque Exerted on Wheel*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3)))/(pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end)). This formula also uses Archimedes' constant .

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Total Angle of Twist for Shaft Formula

Total Angle of Twist for Shaft Example

Total Angle of Twist for Shaft Solution

Total Angle of Twist for Shaft Formula Elements

Other formulas in Torsion of Tapering Shafts category

How to Evaluate Total Angle of Twist for Shaft?

FAQs on Total Angle of Twist for Shaft

Variable Name