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Torque When Strain Energy in the Rod When Subjected to External Torque is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft)
τ = sqrt(U*J*C/l)
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Strain Energy - The Strain energy is defined as the energy stored in a body due to deformation. (Measured in Joule)
Polar moment of Inertia - The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape. (Measured in Kilogram Meter²)
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)
Length of Shaft - The Length of Shaft is the distance between two ends of shaft. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Strain Energy: 50 Joule --> 50 Joule No Conversion Required
Polar moment of Inertia: 50 Kilogram Meter² --> 50 Kilogram Meter² No Conversion Required
Modulus of rigidity: 50 Newton per Square Meter --> 50 Pascal (Check conversion here)
Length of Shaft: 50 Meter --> 50 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
τ = sqrt(U*J*C/l) --> sqrt(50*50*50/50)
Evaluating ... ...
τ = 50
STEP 3: Convert Result to Output's Unit
50 Newton Meter --> No Conversion Required
FINAL ANSWER
50 Newton Meter <-- Torque
(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

Torque When Strain Energy in the Rod When Subjected to External Torque is Given Formula

torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft)
τ = sqrt(U*J*C/l)

Define Torque?

Torque is the measure of the force that can cause an object to rotate about an axis. Force is what causes an object to accelerate in linear kinematics. Similarly, torque is what causes an angular acceleration. Hence, torque can be defined as the rotational equivalent of linear force. The point where the object rotates is called the axis of rotation.

How to Calculate Torque When Strain Energy in the Rod When Subjected to External Torque is Given?

Torque When Strain Energy in the Rod When Subjected to External Torque is Given calculator uses torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft) to calculate the Torque, The Torque When Strain Energy in the Rod When Subjected to External Torque is Given formula is defined as the measure of the force that can cause an object to rotate about an axis. Force is what causes an object to accelerate in linear kinematics. Torque and is denoted by τ symbol.

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

FAQ

What is Torque When Strain Energy in the Rod When Subjected to External Torque is Given?
The Torque When Strain Energy in the Rod When Subjected to External Torque is Given formula is defined as the measure of the force that can cause an object to rotate about an axis. Force is what causes an object to accelerate in linear kinematics and is represented as τ = sqrt(U*J*C/l) or torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft). The Strain energy is defined as the energy stored in a body due to deformation, The Polar moment of Inertia is a shaft or beam's resistance to being distorted by torsion, as a function of its shape, 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 and The Length of Shaft is the distance between two ends of shaft.
How to calculate Torque When Strain Energy in the Rod When Subjected to External Torque is Given?
The Torque When Strain Energy in the Rod When Subjected to External Torque is Given formula is defined as the measure of the force that can cause an object to rotate about an axis. Force is what causes an object to accelerate in linear kinematics is calculated using torque = sqrt(Strain Energy*Polar moment of Inertia*Modulus of rigidity/Length of Shaft). To calculate Torque When Strain Energy in the Rod When Subjected to External Torque is Given, you need Strain Energy (U), Polar moment of Inertia (J), Modulus of rigidity (C) and Length of Shaft (l). With our tool, you need to enter the respective value for Strain Energy, Polar moment of Inertia, Modulus of rigidity and 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 Strain Energy, Polar moment of Inertia, Modulus of rigidity and Length of Shaft. 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 Torque When Strain Energy in the Rod When Subjected to External Torque is Given calculator used?
Among many, Torque When Strain Energy in the Rod When Subjected to External Torque is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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