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)
Jshaft = (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
Jshaft = (τ*L)/(C*θ) --> (50*7)/(84000000000*30)
Evaluating ... ...
Jshaft = 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 00.020 seconds)

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

Modulus of Rigidity of Shaft given Torque Transmitted and Polar Moment of Inertia
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
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
Go Angle of twist = (Torque Exerted on Wheel*Length of Shaft)/(Modulus of Rigidity*Polar Moment of Inertia of shaft)
Torque Transmitted by Shaft given Polar Moment of Inertia and Modulus of Rigidity
Go Torque Exerted on Wheel = (Modulus of Rigidity*Angle of twist*Polar Moment of Inertia of shaft)/Length of Shaft
Length of Shaft given Polar Moment of Inertia and Modulus of Rigidity
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
Go Polar Moment of Inertia of shaft = (Torque Exerted on Wheel*Radius of Shaft)/Maximum Shear Stress on Shaft
Maximum shear stress in shaft given polar moment of inertia
Go Maximum Shear Stress on Shaft = (Torque Exerted on Wheel*Radius of Shaft)/Polar Moment of Inertia of shaft
Torque transmitted by shaft given polar moment of inertia
Go Torque Exerted on Wheel = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Radius of Shaft
Radius of shaft given polar moment of inertia
Go Radius of Shaft = (Maximum Shear Stress on Shaft*Polar Moment of Inertia of shaft)/Torque Exerted on Wheel
Diameter of shaft given polar moment of inertia of shaft
Go Diameter of Shaft = ((32*Polar Moment of Inertia of shaft)/pi)^(1/4)
Polar moment of inertia of shaft
Go Polar Moment of Inertia of shaft = (pi*Diameter of Shaft^4)/32

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

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