Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Calculator

✖Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.ⓘ Torsional moment on shaft [τ]			+10% -10%
✖Length of shaft is defined as the distance between the two opposite ends of a shaft.ⓘ Length of Shaft [l]			+10% -10%
✖Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion.ⓘ Polar moment of inertia for circular section [J]			+10% -10%
✖Modulus of Rigidity 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.ⓘ Modulus of Rigidity [C]			+10% -10%

✖Angle of twist of shaft is the angle through which the fixed end of a shaft rotates with respect to the free end.ⓘ Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia [θ]

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Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity)
θ = (τ*l)/(J*C)
This formula uses 5 Variables

Variables Used

Angle of twist of shaft - (Measured in Radian) - Angle of twist of shaft is the angle through which the fixed end of a shaft rotates with respect to the free end.
Torsional moment on shaft - (Measured in Newton Meter) - Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force.
Length of Shaft - (Measured in Meter) - Length of shaft is defined as the distance between the two opposite ends of a shaft.
Polar moment of inertia for circular section - (Measured in Meter⁴) - Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity 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.

STEP 1: Convert Input(s) to Base Unit

Torsional moment on shaft: 51000 Newton Millimeter --> 51 Newton Meter (Check conversion here)
Length of Shaft: 1100 Millimeter --> 1.1 Meter (Check conversion here)
Polar moment of inertia for circular section: 38000 Millimeter⁴ --> 3.8E-08 Meter⁴ (Check conversion here)
Modulus of Rigidity: 84000 Newton per Square Millimeter --> 84000000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = (τ*l)/(J*C) --> (51*1.1)/(3.8E-08*84000000000)

Evaluating ... ...

θ = 0.0175751879699248

STEP 3: Convert Result to Output's Unit

0.0175751879699248 Radian --> No Conversion Required

FINAL ANSWER

0.0175751879699248 ≈ 0.017575 Radian <-- Angle of twist of shaft

(Calculation completed in 00.020 seconds)

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Home » Engineering » Mechanical » Machine Design » Design Against Static Load » Design of Shaft for Torsional Moment » Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia

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< Design of Shaft for Torsional Moment Calculators

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia

LaTeX Go Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity)

Torsional shear stress in shaft due to torsional moment

LaTeX Go Torsional shear stress in twisted shaft = Torsional moment on shaft*Radial Distance from Axis of Rotation/Polar moment of inertia for circular section

Polar moment of inertia of hollow circular cross-section

LaTeX Go Polar moment of inertia for circular section = pi*((Outer Diameter of Hollow Circular Section^4)-(Inner Diameter of Hollow Circular Section^4))/32

Polar moment of inertia of circular cross section

LaTeX Go Polar moment of inertia for circular section = pi*(Diameter of circular section of shaft^4)/32

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia Formula

LaTeX Go

Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity)
θ = (τ*l)/(J*C)

What is angle of twist?

For a shaft under torsional loading, the angle through which the fixed end of a shaft rotates with respect to the free end is called the angle of twist.

How to Calculate Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia?

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia calculator uses Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity) to calculate the Angle of twist of shaft, Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia formula is defined as the angle through which the shaft is twisted about its central axis when torque is applied onto it or torsion is acting onto the shaft. Angle of twist of shaft is denoted by θ symbol.

How to calculate Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia using this online calculator? To use this online calculator for Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia, enter Torsional moment on shaft (τ), Length of Shaft (l), Polar moment of inertia for circular section (J) & Modulus of Rigidity (C) and hit the calculate button. Here is how the Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia calculation can be explained with given input values -> 0.017575 = (51*1.1)/(3.8E-08*84000000000).

FAQ

What is Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia?

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia formula is defined as the angle through which the shaft is twisted about its central axis when torque is applied onto it or torsion is acting onto the shaft and is represented as θ = (τ*l)/(J*C) or Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity). Torsional moment on shaft is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force, Length of shaft is defined as the distance between the two opposite ends of a shaft, Polar moment of inertia for circular section is the measure of the specimen's resistance to torsion & Modulus of Rigidity 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.

How to calculate Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia?

Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia formula is defined as the angle through which the shaft is twisted about its central axis when torque is applied onto it or torsion is acting onto the shaft is calculated using Angle of twist of shaft = (Torsional moment on shaft*Length of Shaft)/(Polar moment of inertia for circular section*Modulus of Rigidity). To calculate Angle of twist of shaft in radians given torque, length of shaft, polar moment of inertia, you need Torsional moment on shaft (τ), Length of Shaft (l), Polar moment of inertia for circular section (J) & Modulus of Rigidity (C). With our tool, you need to enter the respective value for Torsional moment on shaft, Length of Shaft, Polar moment of inertia for circular section & Modulus of Rigidity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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