Polar moment of inertia of shaft given torque transmitted by shaft 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%
✖Radius of shaft is the distance between the center and the circumference of the shaft.ⓘ Radius of Shaft [R_shaft]			+10% -10%
✖Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.ⓘ Maximum Shear Stress on Shaft [𝜏_max]			+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 by shaft [J_shaft]

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Polar moment of inertia of shaft given torque transmitted by shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft
J_shaft = (τ*R_shaft)/𝜏_max
This formula uses 4 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.
Radius of Shaft - (Measured in Meter) - Radius of shaft is the distance between the center and the circumference of the shaft.
Maximum Shear Stress on Shaft - (Measured in Pascal) - Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.

STEP 1: Convert Input(s) to Base Unit

Torque Exerted on Wheel: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Radius of Shaft: 1350 Millimeter --> 1.35 Meter (Check conversion here)
Maximum Shear Stress on Shaft: 0.0001 Megapascal --> 100 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

J_shaft = (τ*R_shaft)/𝜏_max --> (50*1.35)/100

Evaluating ... ...

J_shaft = 0.675

STEP 3: Convert Result to Output's Unit

0.675 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.675 Meter⁴ <-- Polar Moment of Inertia of shaft

(Calculation completed in 00.004 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 by shaft

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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 by shaft Formula

LaTeX Go

Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft
J_shaft = (τ*R_shaft)/𝜏_max

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 by shaft?

Polar moment of inertia of shaft given torque transmitted by shaft calculator uses Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft to calculate the Polar Moment of Inertia of shaft, Polar moment of inertia of shaft given torque transmitted by shaft 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 by shaft using this online calculator? To use this online calculator for Polar moment of inertia of shaft given torque transmitted by shaft, enter Torque Exerted on Wheel (τ), Radius of Shaft (R_shaft) & Maximum Shear Stress on Shaft (𝜏_max) and hit the calculate button. Here is how the Polar moment of inertia of shaft given torque transmitted by shaft calculation can be explained with given input values -> 0.675 = (50*1.35)/100.

FAQ

What is Polar moment of inertia of shaft given torque transmitted by shaft?

Polar moment of inertia of shaft given torque transmitted by shaft 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*R_shaft)/𝜏_max or Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft. 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, Radius of shaft is the distance between the center and the circumference of the shaft & Maximum Shear Stress on Shaft that acts coplanar with a cross-section of material arises due to shear forces.

How to calculate Polar moment of inertia of shaft given torque transmitted by shaft?

Polar moment of inertia of shaft given torque transmitted by shaft 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*Radius of Shaft)/Maximum Shear Stress on Shaft. To calculate Polar moment of inertia of shaft given torque transmitted by shaft, you need Torque Exerted on Wheel (τ), Radius of Shaft (R_shaft) & Maximum Shear Stress on Shaft (𝜏_max). With our tool, you need to enter the respective value for Torque Exerted on Wheel, Radius of Shaft & Maximum Shear Stress on 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 Polar Moment of Inertia of shaft?

In this formula, Polar Moment of Inertia of shaft uses Torque Exerted on Wheel, Radius of Shaft & Maximum Shear Stress on Shaft. 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*Length of Shaft)/(Modulus of Rigidity*Angle of twist)
Polar Moment of Inertia of shaft = (pi*Diameter of Shaft^4)/32

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