Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Calculator

✖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.ⓘ Torque Exerted on Wheel [τ]			+10% -10%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+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 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 of shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity [J_shaft]

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Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist)
J_shaft = (τ*L)/(C*θ)
This formula uses 5 Variables

Variables Used

Polar Moment of Inertia of shaft - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.
Torque Exerted on Wheel - (Measured in Newton Meter) - 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.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
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.
Angle of twist - Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.

STEP 1: Convert Input(s) to Base Unit

Torque Exerted on Wheel: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Modulus of Rigidity: 84000 Newton per Square Millimeter --> 84000000000 Pascal (Check conversion here)
Angle of twist: 30 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J_shaft = (τ*L)/(C*θ) --> (50*7)/(84000000000*30)

Evaluating ... ...

J_shaft = 1.38888888888889E-10

STEP 3: Convert Result to Output's Unit

1.38888888888889E-10 Meter⁴ --> No Conversion Required

FINAL ANSWER

1.38888888888889E-10 ≈ 1.4E-10 Meter⁴ <-- Polar Moment of Inertia of shaft

(Calculation completed in 00.007 seconds)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Mechanical » Expression for Torque in terms of Polar Moment of Inertia » Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity

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< Expression for Torque in terms of Polar Moment of Inertia Calculators

Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia

LaTeX Go Modulus of Rigidity = (Torque Exerted on Wheel*Length of Shaft)/(Angle of twist*Polar Moment of Inertia of shaft)

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity

LaTeX Go Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist)

Angle of Twist for Shaft given Polar Moment of Inertia and Modulus of Rigidity

LaTeX Go Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft)

Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity

LaTeX Go Length of Shaft = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity Formula

LaTeX Go

Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist)
J_shaft = (τ*L)/(C*θ)

What is difference between moment of inertia and polar moment of inertia?

The main difference between the moment of inertia and the polar moment of inertia is that the moment of inertia measures how an object resists angular acceleration, whereas the polar moment of inertia measures how an object resists torsion.

How to Calculate Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity?

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity calculator uses Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist) to calculate the Polar Moment of Inertia of shaft, Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation. Polar Moment of Inertia of shaft is denoted by J_shaft symbol.

How to calculate Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity using this online calculator? To use this online calculator for Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity, enter Torque Exerted on Wheel (τ), Length of Shaft (L), Modulus of Rigidity (C) & Angle of twist (θ) and hit the calculate button. Here is how the Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity calculation can be explained with given input values -> 1.4E-10 = (50*7)/(84000000000*30).

FAQ

What is Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity?

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation and is represented as J_shaft = (τ*L)/(C*θ) or Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist). 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, The Length of Shaft is the distance between two ends of shaft, 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 & Angle of twist is the angle through which the fixed end of a shaft rotates with respect to the free end.

How to calculate Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity?

Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity is defined as a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of the cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation is calculated using Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Angle of twist). To calculate Polar Moment of Inertia of Shaft given Torque Transmitted and Modulus of Rigidity, you need Torque Exerted on Wheel (τ), Length of Shaft (L), Modulus of Rigidity (C) & Angle of twist (θ). With our tool, you need to enter the respective value for Torque Exerted on Wheel, Length of Shaft, Modulus of Rigidity & Angle of twist 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 Polar Moment of Inertia of shaft?

In this formula, Polar Moment of Inertia of shaft uses Torque Exerted on Wheel, Length of Shaft, Modulus of Rigidity & Angle of twist. We can use 2 other way(s) to calculate the same, which is/are as follows -

Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft
Polar Moment of Inertia of shaft = (pi*Diameter of Shaft^4)/32

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