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Torque on Shaft given Total Angle of Twist for Shaft Formula

GoTorque on Tapering Shaft Formula

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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. Check FAQs

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}})}

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

Torque on Shaft given Total Angle of Twist for Shaft Example

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

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

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

1159.2065 = \frac{30 \cdot 3.1416 \cdot 4E-5 \cdot (5000 - 3000)}{32 \cdot 7000 \cdot (\frac{1}{3000^{3}} - \frac{1}{5000^{3}})}

1159.2065N*m = \frac{30 \cdot 3.1416 \cdot 4E-5MPa \cdot (5000mm - 3000mm)}{32 \cdot 7000mm \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}

1159.2065 = \frac{30 \cdot 3.1416 \cdot 4E-5 \cdot (5000 - 3000)}{32 \cdot 7000 \cdot (\frac{1}{3000^{3}} - \frac{1}{5000^{3}})}

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Torque on Shaft given Total Angle of Twist for Shaft Solution

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

FIRST Step Consider the formula

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}})}

Next Step Substitute values of Variables

∴

τ = \frac{30 \cdot π \cdot 4E-5MPa \cdot (5000mm - 3000mm)}{32 \cdot 7000mm \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}

Next Step Substitute values of Constants

∴

τ = \frac{30 \cdot 3.1416 \cdot 4E-5MPa \cdot (5000mm - 3000mm)}{32 \cdot 7000mm \cdot (\frac{1}{{3000mm}^{3}} - \frac{1}{{5000mm}^{3}})}

Next Step Convert Units

∴

τ = \frac{30 \cdot 3.1416 \cdot 40Pa \cdot (5m - 3m)}{32 \cdot 7m \cdot (\frac{1}{{3m}^{3}} - \frac{1}{{5m}^{3}})}

Next Step Prepare to Evaluate

∴

τ = \frac{30 \cdot 3.1416 \cdot 40 \cdot (5 - 3)}{32 \cdot 7 \cdot (\frac{1}{3^{3}} - \frac{1}{5^{3}})}

Next Step Evaluate

∴

τ = 1159.20647294448N*m

LAST Step Rounding Answer

∴

τ = 1159.2065N*m

Torque on Shaft given Total Angle of Twist for Shaft Formula Elements

Variables

Constants

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

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

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

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

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

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

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 to find Torque Exerted on Wheel

Go Torque on Tapering Shaft

τ = \frac{𝜏 \cdot π \cdot d s}{16}

Other formulas in Torsion of Tapering Shafts category

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 Total Angle of Twist for Shaft

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)}

Go Modulus of Rigidity of Shaft given Total Angle of Twist for Shaft

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

How to Evaluate Torque on Shaft given Total Angle of Twist for Shaft?

Torque on Shaft given Total Angle of Twist for Shaft evaluator uses Torque Exerted on Wheel = (Angle of twist*pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end))/(32*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3))) to evaluate the Torque Exerted on Wheel, Torque on shaft given total angle of twist for shaft is the measure of the force that can cause an object to rotate about an axis. Torque Exerted on Wheel is denoted by τ symbol.

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

FAQs on Torque on Shaft given Total Angle of Twist for Shaft

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

The formula of Torque on Shaft given Total Angle of Twist for Shaft is expressed as Torque Exerted on Wheel = (Angle of twist*pi*Modulus of rigidity of Shaft*(Diameter of shaft at right end-Diameter of shaft at left end))/(32*Length of Shaft*(1/(Diameter of shaft at left end^3)-1/(Diameter of shaft at right end^3))). Here is an example- 1159.206 = (30*pi*40*(5-3))/(32*7*(1/(3^3)-1/(5^3))).

How to calculate Torque on Shaft given Total Angle of Twist for Shaft?

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

What are the other ways to Calculate Torque Exerted on Wheel?

Here are the different ways to Calculate Torque Exerted on Wheel-

Torque Exerted on Wheel=(Shear stress on surface of shaft*pi*Diameter of Shaft)/16

Can the Torque on Shaft given Total Angle of Twist for Shaft be negative?

No, the Torque on Shaft given Total Angle of Twist for Shaft, measured in Torque cannot be negative.

Which unit is used to measure Torque on Shaft given Total Angle of Twist for Shaft?

Torque on Shaft given Total Angle of Twist for Shaft is usually measured using the Newton Meter[N*m] for Torque. Newton Centimeter[N*m], Newton Millimeter[N*m], Kilonewton Meter[N*m] are the few other units in which Torque on Shaft given Total Angle of Twist for Shaft can be measured.

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Torque on Shaft given Total Angle of Twist for Shaft Formula

​GoTorque on Tapering Shaft Formula

Torque on Shaft given Total Angle of Twist for Shaft Example

Torque on Shaft given Total Angle of Twist for Shaft Solution

Torque on Shaft given Total Angle of Twist for Shaft Formula Elements

Other Formulas to find Torque Exerted on Wheel

Other formulas in Torsion of Tapering Shafts category

How to Evaluate Torque on Shaft given Total Angle of Twist for Shaft?

FAQs on Torque on Shaft given Total Angle of Twist for Shaft

Variable Name

GoTorque on Tapering Shaft Formula