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 = (GTorsion*θ*J)/Lshaft
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 = (GTorsion*θ*J)/Lshaft --> (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 00.020 seconds)

Credits

Created by Rithik Agrawal
National Institute of Technology Karnataka (NITK), Surathkal
Rithik Agrawal has created this Calculator and 1300+ more calculators!
Verified by Mithila Muthamma PA
Coorg Institute of Technology (CIT), Coorg
Mithila Muthamma PA has verified this Calculator and 700+ more calculators!

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

Twisting Moment given Polar MOI and Twist Angle Formula

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

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 (GTorsion), Angle of Twist (θ), Polar Moment of Inertia (J) & Length of Shaft (Lshaft) 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 = (GTorsion*θ*J)/Lshaft 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 (GTorsion), Angle of Twist (θ), Polar Moment of Inertia (J) & Length of Shaft (Lshaft). 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
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!