Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System Calculator

✖Frequency is the number of times something happens in a particular period.ⓘ Frequency [f]			+10% -10%
✖The Length of Shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L]			+10% -10%
✖Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.ⓘ Moment of inertia of Shaft [I_shaft]			+10% -10%
✖Polar Moment of Inertia of Shaft is the measure of object resistance to torsion.ⓘ Polar Moment of Inertia of Shaft [J_shaft]			+10% -10%

✖Modulus of Rigidity represents the elastic coefficient that causes lateral deformation when a shear force is applied to a body. It is an indicator of a body's rigidity.ⓘ Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System [G]

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Formula

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Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System

Formula

`"G" = ((2*pi*"f")^2*"L"*"I"_{"shaft"})/"J"_{"shaft"}`

Example

`"39.79424N/m²"=((2*pi*"0.120Hz")^2*"7000mm"*"100kg·m²")/"10m⁴"`

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Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft
G = ((2*pi*f)^2*L*I_shaft)/J_shaft
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity represents the elastic coefficient that causes lateral deformation when a shear force is applied to a body. It is an indicator of a body's rigidity.
Frequency - (Measured in Hertz) - Frequency is the number of times something happens in a particular period.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Moment of inertia of Shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
Polar Moment of Inertia of Shaft - (Measured in Meter⁴) - Polar Moment of Inertia of Shaft is the measure of object resistance to torsion.

STEP 1: Convert Input(s) to Base Unit

Frequency: 0.12 Hertz --> 0.12 Hertz No Conversion Required
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Moment of inertia of Shaft: 100 Kilogram Square Meter --> 100 Kilogram Square Meter No Conversion Required
Polar Moment of Inertia of Shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G = ((2*pi*f)^2*L*I_shaft)/J_shaft --> ((2*pi*0.12)^2*7*100)/10

Evaluating ... ...

G = 39.7942449451923

STEP 3: Convert Result to Output's Unit

39.7942449451923 Pascal -->39.7942449451923 Newton per Square Meter (Check conversion here)

FINAL ANSWER

39.7942449451923 ≈ 39.79424 Newton per Square Meter <-- Modulus of Rigidity

(Calculation completed in 00.007 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Free Torsional Vibrations of Rotor Systems » Free Torsional Vibrations of Single Rotor System » Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System

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< 2 Free Torsional Vibrations of Single Rotor System Calculators

Natural Frequency of Free Torsional Vibration of Single Rotor System

Go Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi)

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System

Go Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System Formula

Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft
G = ((2*pi*f)^2*L*I_shaft)/J_shaft

What is the difference between free and forced vibration?

Free vibrations involve no transfer of energy between the vibrating object and its surroundings, whereas forced vibrations occur when there's an external driving force and thus transfer of energy between the vibrating object and its surroundings.

How to Calculate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System calculator uses Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft to calculate the Modulus of Rigidity, The Modulus of rigidity of shaft for free torsional vibration of single rotor system formula is defined as the measure of the rigidity of the body. Modulus of Rigidity is denoted by G symbol.

How to calculate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System using this online calculator? To use this online calculator for Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System, enter Frequency (f), Length of Shaft (L), Moment of inertia of Shaft (I_shaft) & Polar Moment of Inertia of Shaft (J_shaft) and hit the calculate button. Here is how the Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System calculation can be explained with given input values -> 39.79424 = ((2*pi*0.12)^2*7*100)/10.

FAQ

What is Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

The Modulus of rigidity of shaft for free torsional vibration of single rotor system formula is defined as the measure of the rigidity of the body and is represented as G = ((2*pi*f)^2*L*I_shaft)/J_shaft or Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft. Frequency is the number of times something happens in a particular period, The Length of Shaft is the distance between two ends of shaft, Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation & Polar Moment of Inertia of Shaft is the measure of object resistance to torsion.

How to calculate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

The Modulus of rigidity of shaft for free torsional vibration of single rotor system formula is defined as the measure of the rigidity of the body is calculated using Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft. To calculate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System, you need Frequency (f), Length of Shaft (L), Moment of inertia of Shaft (I_shaft) & Polar Moment of Inertia of Shaft (J_shaft). With our tool, you need to enter the respective value for Frequency, Length of Shaft, Moment of inertia of Shaft & Polar Moment of Inertia of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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