Polar Modulus of Hollow Shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Zp = (pi*((do^4)-(di^4)))/(16*do)
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Polar Modulus - (Measured in Cubic Meter) - The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.
Outer Diameter of Shaft - (Measured in Meter) - Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.
Inner Dia of Shaft - (Measured in Meter) - The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.
STEP 1: Convert Input(s) to Base Unit
Outer Diameter of Shaft: 700 Millimeter --> 0.7 Meter (Check conversion here)
Inner Dia of Shaft: 0.688 Meter --> 0.688 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Zp = (pi*((do^4)-(di^4)))/(16*do) --> (pi*((0.7^4)-(0.688^4)))/(16*0.7)
Evaluating ... ...
Zp = 0.00450074035006326
STEP 3: Convert Result to Output's Unit
0.00450074035006326 Cubic Meter --> No Conversion Required
FINAL ANSWER
0.00450074035006326 0.004501 Cubic Meter <-- Polar Modulus
(Calculation completed in 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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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 Modulus of Hollow Shaft Formula

Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Zp = (pi*((do^4)-(di^4)))/(16*do)

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 Modulus of Hollow Shaft?

Polar Modulus of Hollow Shaft calculator uses Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft) to calculate the Polar Modulus, The Polar Modulus of Hollow Shaft formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called as torsional section modulus. It is denoted by Z p. Polar Modulus is denoted by Zp symbol.

How to calculate Polar Modulus of Hollow Shaft using this online calculator? To use this online calculator for Polar Modulus of Hollow Shaft, enter Outer Diameter of Shaft (do) & Inner Dia of Shaft (di) and hit the calculate button. Here is how the Polar Modulus of Hollow Shaft calculation can be explained with given input values -> 0.004501 = (pi*((0.7^4)-(0.688^4)))/(16*0.7).

FAQ

What is Polar Modulus of Hollow Shaft?
The Polar Modulus of Hollow Shaft formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called as torsional section modulus. It is denoted by Z p and is represented as Zp = (pi*((do^4)-(di^4)))/(16*do) or Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft). Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft & The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.
How to calculate Polar Modulus of Hollow Shaft?
The Polar Modulus of Hollow Shaft formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called as torsional section modulus. It is denoted by Z p is calculated using Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft). To calculate Polar Modulus of Hollow Shaft, you need Outer Diameter of Shaft (do) & Inner Dia of Shaft (di). With our tool, you need to enter the respective value for Outer Diameter of Shaft & Inner 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 Modulus?
In this formula, Polar Modulus uses Outer Diameter of Shaft & Inner Dia of Shaft. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Polar Modulus = Polar Moment of Inertia/Radius of Shaft
  • Polar Modulus = (pi*Dia of Shaft^3)/16
  • Polar Modulus = Polar Moment of Inertia/Radius of Shaft
  • Polar Modulus = (pi*Dia of Shaft^3)/16
  • Polar Modulus = (Torque/Maximum Shear Stress)
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