Moment of Inertia of Disc using Natural Frequency of Vibration Calculator

✖torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.ⓘ Torsional Stiffness [q]			+10% -10%
✖Natural Frequency is the number of oscillations or cycles per second in a torsional vibration system, characterizing its inherent oscillatory behavior.ⓘ Natural Frequency [f_n]			+10% -10%

✖Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.ⓘ Moment of Inertia of Disc using Natural Frequency of Vibration [I_d]

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Moment of Inertia of Disc using Natural Frequency of Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2)
I_d = q/((2*pi*f_n)^2)
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Mass Moment of Inertia of Disc - (Measured in Kilogram Square Meter) - Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.
Torsional Stiffness - (Measured in Newton per Meter) - torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.
Natural Frequency - (Measured in Hertz) - Natural Frequency is the number of oscillations or cycles per second in a torsional vibration system, characterizing its inherent oscillatory behavior.

STEP 1: Convert Input(s) to Base Unit

Torsional Stiffness: 5.4 Newton per Meter --> 5.4 Newton per Meter No Conversion Required
Natural Frequency: 0.148532 Hertz --> 0.148532 Hertz No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_d = q/((2*pi*f_n)^2) --> 5.4/((2*pi*0.148532)^2)

Evaluating ... ...

I_d = 6.20003248918117

STEP 3: Convert Result to Output's Unit

6.20003248918117 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

6.20003248918117 ≈ 6.200032 Kilogram Square Meter <-- Mass Moment of Inertia of Disc

(Calculation completed in 00.011 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Mechanical » Natural Frequency of Free Torsional Vibrations » Moment of Inertia of Disc using Natural Frequency of Vibration

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< Natural Frequency of Free Torsional Vibrations Calculators

Moment of Inertia of Disc using Natural Frequency of Vibration

LaTeX Go Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2)

Torsional Stiffness of Shaft given Natural Frequency of Vibration

LaTeX Go Torsional Stiffness = (2*pi*Natural Frequency)^2*Mass Moment of Inertia of Disc

Torsional Stiffness of Shaft given Time Period of Vibration

LaTeX Go Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2

Moment of Inertia of Disc given Time Period of Vibration

LaTeX Go Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)

Moment of Inertia of Disc using Natural Frequency of Vibration Formula

LaTeX Go

Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2)
I_d = q/((2*pi*f_n)^2)

What causes torsional vibration?

Torsional vibrations are an example of machinery vibrations and are caused by the superposition of angular oscillations along the whole propulsion shaft system including propeller shaft, engine crankshaft, engine, gearbox, flexible coupling and along the intermediate shafts.

How to Calculate Moment of Inertia of Disc using Natural Frequency of Vibration?

Moment of Inertia of Disc using Natural Frequency of Vibration calculator uses Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2) to calculate the Mass Moment of Inertia of Disc, Moment of Inertia of Disc using Natural Frequency of Vibration formula is defined as a measure of an object's resistance to changes in its rotation, calculated using the natural frequency of vibration, providing valuable insights into the disc's rotational motion and stability in torsional vibrations. Mass Moment of Inertia of Disc is denoted by I_d symbol.

How to calculate Moment of Inertia of Disc using Natural Frequency of Vibration using this online calculator? To use this online calculator for Moment of Inertia of Disc using Natural Frequency of Vibration, enter Torsional Stiffness (q) & Natural Frequency (f_n) and hit the calculate button. Here is how the Moment of Inertia of Disc using Natural Frequency of Vibration calculation can be explained with given input values -> 6.200032 = 5.4/((2*pi*0.148532)^2).

FAQ

What is Moment of Inertia of Disc using Natural Frequency of Vibration?

Moment of Inertia of Disc using Natural Frequency of Vibration formula is defined as a measure of an object's resistance to changes in its rotation, calculated using the natural frequency of vibration, providing valuable insights into the disc's rotational motion and stability in torsional vibrations and is represented as I_d = q/((2*pi*f_n)^2) or Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2). torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque & Natural Frequency is the number of oscillations or cycles per second in a torsional vibration system, characterizing its inherent oscillatory behavior.

How to calculate Moment of Inertia of Disc using Natural Frequency of Vibration?

Moment of Inertia of Disc using Natural Frequency of Vibration formula is defined as a measure of an object's resistance to changes in its rotation, calculated using the natural frequency of vibration, providing valuable insights into the disc's rotational motion and stability in torsional vibrations is calculated using Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2). To calculate Moment of Inertia of Disc using Natural Frequency of Vibration, you need Torsional Stiffness (q) & Natural Frequency (f_n). With our tool, you need to enter the respective value for Torsional Stiffness & Natural Frequency 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 Mass Moment of Inertia of Disc?

In this formula, Mass Moment of Inertia of Disc uses Torsional Stiffness & Natural Frequency. We can use 2 other way(s) to calculate the same, which is/are as follows -

Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)
Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2)

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