Polar Modulus of Hollow Shaft Calculator

✖Outer Diameter of Shaft is the length of the longest chord of the surface of the hollow circular shaft.ⓘ Outer Diameter of Shaft [d_o]			+10% -10%
✖The Inner Dia of Shaft is defined as the Diameter that is length of the longest chord inside the hollow shaft.ⓘ Inner Dia of Shaft [d_i]			+10% -10%

✖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.ⓘ Polar Modulus of Hollow Shaft [Z_p]

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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)
Z_p = (pi*((d_o^4)-(d_i^4)))/(16*d_o)
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

Z_p = (pi*((d_o^4)-(d_i^4)))/(16*d_o) --> (pi*((0.7^4)-(0.688^4)))/(16*0.7)

Evaluating ... ...

Z_p = 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)

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Home » Physics » Strength of Materials » Torsion of Shafts And Springs » Mechanical » Polar Modulus » Polar Modulus of Hollow Shaft

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Polar Modulus Calculators

Polar Moment of Inertia using Polar Modulus

LaTeX Go Polar Moment of Inertia = Radius of Shaft*Polar Modulus

Radius of Shaft using Polar Modulus

LaTeX Go Radius of Shaft = Polar Moment of Inertia/Polar Modulus

Polar Modulus

LaTeX Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Polar Moment of Inertia of Solid Shaft

LaTeX Go Polar Moment of Inertia = (pi*Dia of Shaft^4)/32

< Polar Modulus Calculators

Inner diameter of Hollow Shaft using Polar Modulus

LaTeX 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

LaTeX Go Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)

Polar Modulus

LaTeX Go Polar Modulus = Polar Moment of Inertia/Radius of Shaft

Diameter of Solid Shaft with known Polar Modulus

LaTeX Go Dia of Shaft = ((16*Polar Modulus)/pi)^(1/3)

Polar Modulus of Hollow Shaft Formula

LaTeX Go

Polar Modulus = (pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Z_p = (pi*((d_o^4)-(d_i^4)))/(16*d_o)

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 Z_p 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 (d_o) & Inner Dia of Shaft (d_i) 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 Z_p = (pi*((d_o^4)-(d_i^4)))/(16*d_o) 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 (d_o) & Inner Dia of Shaft (d_i). 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 3 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

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