Twist angle given Shaft length and modulus of rigidity Calculator

✖Torque is a measure of the force that can cause an object to rotate about an axis.ⓘ Torque [T]			+10% -10%
✖Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%
✖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.ⓘ Polar Moment of Inertia [J]			+10% -10%
✖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.ⓘ Modulus of Rigidity [G_Torsion]			+10% -10%

✖Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.ⓘ Twist angle given Shaft length and modulus of rigidity [θ]

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Formula

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Twist angle given Shaft length and modulus of rigidity

Formula

`"θ" = ("T"*"L"_{"shaft"})/("J"*"G"_{"Torsion"})`

Example

`"0.000782rad"=("28kN*m"*"4.58m")/("4.1e-3m⁴"*"40GPa")`

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Twist angle given Shaft length and modulus of rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity)
θ = (T*L_shaft)/(J*G_Torsion)
This formula uses 5 Variables

Variables Used

Angle of Twist - (Measured in Radian) - Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.
Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance between two ends of shaft.
Polar Moment of Inertia - (Measured in Meter⁴) - 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.
Modulus of Rigidity - (Measured in Pascal) - 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.

STEP 1: Convert Input(s) to Base Unit

Torque: 28 Kilonewton Meter --> 28000 Newton Meter (Check conversion here)
Length of Shaft: 4.58 Meter --> 4.58 Meter No Conversion Required
Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = (T*L_shaft)/(J*G_Torsion) --> (28000*4.58)/(0.0041*40000000000)

Evaluating ... ...

θ = 0.000781951219512195

STEP 3: Convert Result to Output's Unit

0.000781951219512195 Radian --> No Conversion Required

FINAL ANSWER

0.000781951219512195 ≈ 0.000782 Radian <-- Angle of Twist

(Calculation completed in 00.004 seconds)

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< 18 Torsion Calculators

Shaft length for given maximum permissible shear stress and modulus of rigidity

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

Maximum permissible shear stress for given Radius and modulus of rigidity

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

Modulus of rigidity given maximum permissible shear stress

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

Twist angle given maximum permissible shear stress

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

Shaft length for given Polar MOI, Twisting Moment, Modulus of rigidity, and Twist angle

Go Length of Shaft = (Modulus of Rigidity*(Angle of Twist)*Polar Moment of Inertia)/Torque

Twist angle given Shaft length and modulus of rigidity

Go Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity)

Polar moment of inertia

Go Polar Moment of Inertia = (Torque*Length of Shaft)/(Angle of Twist*Modulus of Rigidity)

Modulus of rigidity

Go Modulus of Rigidity = (Torque*Length of Shaft)/(Angle of Twist*Polar Moment of Inertia)

Twisting Moment given Polar MOI and Twist Angle

Go Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft

Polar Moment of Inertia of Hollow Shaft

Go Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)

Twisting Moment given Maximum Permissible Shear Stress

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

Polar Moment of Inertia given twisting moment along with maximum permissible shear stress

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

Radius given Twisting moment and Polar Moment of Inertia of shaft

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

Radius with known Maximum permissible shear stress

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

Maximum permissible shear stress

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

Radius given Torsional Section Modulus

Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus

Radius of Shaft using Polar Modulus

Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus

Torsional Section Modulus

Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Twist angle given Shaft length and modulus of rigidity Formula

Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity)
θ = (T*L_shaft)/(J*G_Torsion)

What is Torsion?

n the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal, an SI unit for newtons per square metre, or in pounds per square inch while torque is expressed in newton metres or foot-pound force.

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

Twist angle given Shaft length and modulus of rigidity calculator uses Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity) to calculate 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 calculate Twist angle given Shaft length and modulus of rigidity using this online calculator? To use this online calculator 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. Here is how the Twist angle given Shaft length and modulus of rigidity calculation can be explained with given input values -> 0.000782 = (28000*4.58)/(0.0041*40000000000).

FAQ

What is Twist angle given Shaft length and modulus of rigidity?

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 and is represented as θ = (T*L_shaft)/(J*G_Torsion) or Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity). Torque is a measure of the force that can cause an object to rotate about an axis, Length of Shaft is the distance between two ends of shaft, 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 & 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.

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

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 is calculated using Angle of Twist = (Torque*Length of Shaft)/(Polar Moment of Inertia*Modulus of Rigidity). To calculate Twist angle given Shaft length and modulus of rigidity, you need Torque (T), Length of Shaft (L_shaft), Polar Moment of Inertia (J) & Modulus of Rigidity (G_Torsion). With our tool, you need to enter the respective value for Torque, Length of Shaft, Polar Moment of Inertia & Modulus of Rigidity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Angle of Twist?

In this formula, Angle of Twist uses Torque, Length of Shaft, Polar Moment of Inertia & Modulus of Rigidity. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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