Polar Moment of Inertia of Solid Shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
Polar Moment of Inertia = (pi*Dia of Shaft^4)/32
J = (pi*d^4)/32
This formula uses 1 Constants, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Polar Moment of Inertia - (Measured in Meter⁴) - Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.
Dia of Shaft - (Measured in Meter) - The Dia of Shaft is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.
STEP 1: Convert Input(s) to Base Unit
Dia of Shaft: 0.284 Meter --> 0.284 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
J = (pi*d^4)/32 --> (pi*0.284^4)/32
Evaluating ... ...
J = 0.000638665202759738
STEP 3: Convert Result to Output's Unit
0.000638665202759738 Meter⁴ --> No Conversion Required
FINAL ANSWER
0.000638665202759738 0.000639 Meter⁴ <-- Polar Moment of Inertia
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Verified by Payal Priya
Birsa Institute of Technology (BIT), Sindri
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9 Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus
Go Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4)
Polar Modulus of Hollow Shaft
Go Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Polar Moment of Inertia of Hollow Shaft
Go Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)
Polar Moment of Inertia using Polar Modulus
Go Polar Moment of Inertia = Radius of Shaft*Polar Modulus
Radius of Shaft using Polar Modulus
Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus
Polar Modulus
Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft
Polar Moment of Inertia of Solid Shaft
Go Polar Moment of Inertia = (pi*Dia of Shaft^4)/32
Diameter of Solid Shaft with known Polar Modulus
Go Dia of Shaft = ((16*Polar Modulus)/pi)^(1/3)
Polar Modulus of Solid Shaft
Go Polar Modulus = (pi*Dia of Shaft^3)/16

9 Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus
Go Inner Dia of Shaft = ((Outer Diameter of Shaft^4)-((Polar Modulus*16*Outer Diameter of Shaft)/pi))^(1/4)
Polar Modulus of Hollow Shaft
Go Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Polar Moment of Inertia given Torsional Section Modulus
Go Polar Moment of Inertia = Polar Modulus*Radius of Shaft
Polar Moment of Inertia using Polar Modulus
Go Polar Moment of Inertia = Radius of Shaft*Polar Modulus
Polar Modulus
Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft
Polar Moment of Inertia of Solid Shaft
Go Polar Moment of Inertia = (pi*Dia of Shaft^4)/32
Diameter of Solid Shaft with known Polar Modulus
Go Dia of Shaft = ((16*Polar Modulus)/pi)^(1/3)
Polar Modulus using Maximum Twisting Moment
Go Polar Modulus = (Torque/Maximum Shear Stress)
Polar Modulus of Solid Shaft
Go Polar Modulus = (pi*Dia of Shaft^3)/16

Polar Moment of Inertia of Solid Shaft Formula

Polar Moment of Inertia = (pi*Dia of Shaft^4)/32
J = (pi*d^4)/32

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 Solid Shaft?

Polar Moment of Inertia of Solid Shaft calculator uses Polar Moment of Inertia = (pi*Dia of Shaft^4)/32 to calculate the Polar Moment of Inertia, The Polar Moment of Inertia of Solid Shaft formula 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 is denoted by J symbol.

How to calculate Polar Moment of Inertia of Solid Shaft using this online calculator? To use this online calculator for Polar Moment of Inertia of Solid Shaft, enter Dia of Shaft (d) and hit the calculate button. Here is how the Polar Moment of Inertia of Solid Shaft calculation can be explained with given input values -> 0.000639 = (pi*0.284^4)/32.

FAQ

What is Polar Moment of Inertia of Solid Shaft?
The Polar Moment of Inertia of Solid Shaft formula 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 = (pi*d^4)/32 or Polar Moment of Inertia = (pi*Dia of Shaft^4)/32. The Dia of Shaft is the diameter of the external surface of a shaft which is a rotating element in the transmitting system for transmitting power.
How to calculate Polar Moment of Inertia of Solid Shaft?
The Polar Moment of Inertia of Solid Shaft formula 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 = (pi*Dia of Shaft^4)/32. To calculate Polar Moment of Inertia of Solid Shaft, you need Dia of Shaft (d). With our tool, you need to enter the respective value for Dia 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 Polar Moment of Inertia?
In this formula, Polar Moment of Inertia uses Dia of Shaft. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Polar Moment of Inertia = Radius of Shaft*Polar Modulus
  • Polar Moment of Inertia = pi/32*(Outer Diameter of Shaft^4-Inner Dia of Shaft^4)
  • Polar Moment of Inertia = Radius of Shaft*Polar Modulus
  • Polar Moment of Inertia = Polar Modulus*Radius of Shaft
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