Twisting Moment given Polar MOI and Twist Angle Calculator

✖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.ⓘ Angle of Twist [θ]			+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%
✖Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%

✖Torque is a measure of the force that can cause an object to rotate about an axis.ⓘ Twisting Moment given Polar MOI and Twist Angle [T]

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Twisting Moment given Polar MOI and Twist Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Torque - (Measured in Newton Meter) - Torque is a measure of the force that can cause an object to rotate about an axis.
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.
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.
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.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance between two ends of shaft.

STEP 1: Convert Input(s) to Base Unit

Modulus of Rigidity: 40 Gigapascal --> 40000000000 Pascal (Check conversion here)
Angle of Twist: 1.42 Radian --> 1.42 Radian No Conversion Required
Polar Moment of Inertia: 0.0041 Meter⁴ --> 0.0041 Meter⁴ No Conversion Required
Length of Shaft: 4.58 Meter --> 4.58 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = (G_Torsion*θ*J)/L_shaft --> (40000000000*1.42*0.0041)/4.58

Evaluating ... ...

T = 50847161.5720524

STEP 3: Convert Result to Output's Unit

50847161.5720524 Newton Meter -->50847.1615720524 Kilonewton Meter (Check conversion here)

FINAL ANSWER

50847.1615720524 ≈ 50847.16 Kilonewton Meter <-- Torque

(Calculation completed in 00.004 seconds)

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Maximum permissible shear stress for given Radius and modulus of rigidity

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

Twisting Moment given Maximum Permissible Shear Stress

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

Radius with known Maximum permissible shear stress

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

Maximum permissible shear stress

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

Twisting Moment given Polar MOI and Twist Angle Formula

LaTeX Go

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

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 Twisting Moment given Polar MOI and Twist Angle?

Twisting Moment given Polar MOI and Twist Angle calculator uses Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft to calculate 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 calculate Twisting Moment given Polar MOI and Twist Angle using this online calculator? To use this online calculator 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. Here is how the Twisting Moment given Polar MOI and Twist Angle calculation can be explained with given input values -> 50.84716 = (40000000000*1.42*0.0041)/4.58.

FAQ

What is Twisting Moment given Polar MOI and Twist Angle?

The Twisting Moment given Polar MOI and Twist Angle formula is defined as the moment given to the shaft to twist it and is represented as T = (G_Torsion*θ*J)/L_shaft or Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft. 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, Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end, 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 & Length of Shaft is the distance between two ends of shaft.

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

The Twisting Moment given Polar MOI and Twist Angle formula is defined as the moment given to the shaft to twist it is calculated using Torque = (Modulus of Rigidity*Angle of Twist*Polar Moment of Inertia)/Length of Shaft. To calculate Twisting Moment given Polar MOI and Twist Angle, you need Modulus of Rigidity (G_Torsion), Angle of Twist (θ), Polar Moment of Inertia (J) & Length of Shaft (L_shaft). With our tool, you need to enter the respective value for Modulus of Rigidity, Angle of Twist, Polar Moment of Inertia & Length of Shaft 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 Torque?

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

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

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