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## Credits

Osmania University (OU), Hyderabad
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## Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity
J = (τ^2)*l/U*C
This formula uses 4 Variables
Variables Used
Torque - Torque 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. (Measured in Newton Meter)
Length of Shaft - The Length of Shaft is the distance between two ends of shaft. (Measured in Meter)
Strain Energy - The Strain energy is defined as the energy stored in a body due to deformation. (Measured in Joule)
Modulus of rigidity - 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. (Measured in Newton per Square Meter)
STEP 1: Convert Input(s) to Base Unit
Torque: 50 Newton Meter --> 50 Newton Meter No Conversion Required
Length of Shaft: 50 Meter --> 50 Meter No Conversion Required
Strain Energy: 50 Joule --> 50 Joule No Conversion Required
Modulus of rigidity: 50 Newton per Square Meter --> 50 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
J = (τ^2)*l/U*C --> (50^2)*50/50*50
Evaluating ... ...
J = 125000
STEP 3: Convert Result to Output's Unit
125000 Kilogram Meter² --> No Conversion Required
FINAL ANSWER
125000 Kilogram Meter² <-- Polar moment of Inertia
(Calculation completed in 00.016 seconds)

## < 10+ Castigliano's Theorem Calculators

Force Applied on the Rod When Strain Energy Stored in Tension Rod is Given
axial_force = sqrt(Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Length of Rod) Go
Torque When Strain Energy in the Rod When Subjected to External Torque is Given
torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft) Go
Strain Energy Stored in the Rod Subjected to Bending Moment
strain_energy = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Moment of Inertia Go
Modulus of Elasticity of the Rod When Strain Energy Stored is Given
modulus_of_elasticity = Axial Force^2*Length of Rod/2*Cross sectional area*Strain Energy Go
Length of the Rod When Strain Energy Stored is Given
length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2 Go
Strain Energy Stored in Tension Rod
strain_energy = Axial Force^2*Length of Rod/2*Cross sectional area*Modulus Of Elasticity Go
Length of Shaft When Strain Energy in the Shaft Subjected to External Torque
length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2) Go
Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given
polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity Go
Modulus of Rigidity of the Rod When Strain Energy in the Rod is Given
modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy Go
Strain Energy in the Rod When it is Subjected to External Torque
strain_energy = (Torque^2)*Length of Shaft/Polar moment of Inertia*Modulus of rigidity Go

### Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given Formula

polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity
J = (τ^2)*l/U*C

## Define Polar Moment of Inertia?

The polar moment of inertia, also known as second polar moment of area, is a quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects (or segments of cylindrical object) with an invariant cross-section and no significant warping or out-of-plane deformation.[1] It is a constituent of the second moment of area, linked through the perpendicular axis theorem.

## How to Calculate Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given?

Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given calculator uses polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity to calculate the Polar moment of Inertia, The Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given formula is defined as the quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects with an invariant cross-section and no significant warping or out-of-plane deformation. Polar moment of Inertia and is denoted by J symbol.

How to calculate Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given using this online calculator? To use this online calculator for Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given, enter Torque (τ), Length of Shaft (l), Strain Energy (U) and Modulus of rigidity (C) and hit the calculate button. Here is how the Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given calculation can be explained with given input values -> 125000 = (50^2)*50/50*50.

### FAQ

What is Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given?
The Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given formula is defined as the quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects with an invariant cross-section and no significant warping or out-of-plane deformation and is represented as J = (τ^2)*l/U*C or polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity. Torque 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, The Strain energy is defined as the energy stored in a body due to deformation and 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 Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given?
The Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given formula is defined as the quantity used to describe resistance to torsional deformation (deflection), in cylindrical objects with an invariant cross-section and no significant warping or out-of-plane deformation is calculated using polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity. To calculate Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given, you need Torque (τ), Length of Shaft (l), Strain Energy (U) and Modulus of rigidity (C). With our tool, you need to enter the respective value for Torque, Length of Shaft, Strain Energy and Modulus of rigidity 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?
In this formula, Polar moment of Inertia uses Torque, Length of Shaft, Strain Energy and Modulus of rigidity. We can use 10 other way(s) to calculate the same, which is/are as follows -
• strain_energy = Axial Force^2*Length of Rod/2*Cross sectional area*Modulus Of Elasticity
• axial_force = sqrt(Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Length of Rod)
• length_of_rod = Strain Energy*2*Cross sectional area*Modulus Of Elasticity/Axial Force^2
• modulus_of_elasticity = Axial Force^2*Length of Rod/2*Cross sectional area*Strain Energy
• strain_energy = (Torque^2)*Length of Shaft/Polar moment of Inertia*Modulus of rigidity
• torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft)
• length_of_shaft = Strain Energy*Polar moment of Inertia*Modulus of rigidity/(Torque^2)
• modulus_of_rigidity = (Torque^2)*Length of Shaft/Polar moment of Inertia*Strain Energy
• polar_moment_of_inertia = (Torque^2)*Length of Shaft/Strain Energy*Modulus of rigidity
• strain_energy = (Bending moment^2)*Length of Shaft/Modulus Of Elasticity*Moment of Inertia
Where is the Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given calculator used?
Among many, Polar Moment of Inertia of the Rod When Strain Energy in the Rod is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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