Moment of Inertia of Disc given Angular Velocity Calculator

✖Resistance Torsional Stiffness is the resistance of an object to twisting or rotational deformation, measured by the amount of torque required to produce a unit of angular deformation.ⓘ Resistance Torsional Stiffness [q_r]			+10% -10%
✖Angular Velocity is the measure of how quickly an object rotates or revolves around a central axis in a torsional vibration system.ⓘ Angular Velocity [ω]			+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 given Angular Velocity [I_d]

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Moment of Inertia of Disc given Angular Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2)
I_d = q_r/(ω^2)
This formula uses 3 Variables

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.
Resistance Torsional Stiffness - (Measured in Newton per Meter) - Resistance Torsional Stiffness is the resistance of an object to twisting or rotational deformation, measured by the amount of torque required to produce a unit of angular deformation.
Angular Velocity - (Measured in Radian per Second) - Angular Velocity is the measure of how quickly an object rotates or revolves around a central axis in a torsional vibration system.

STEP 1: Convert Input(s) to Base Unit

Resistance Torsional Stiffness: 777.728 Newton per Meter --> 777.728 Newton per Meter No Conversion Required
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_d = q_r/(ω^2) --> 777.728/(11.2^2)

Evaluating ... ...

I_d = 6.2

STEP 3: Convert Result to Output's Unit

6.2 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

6.2 Kilogram Square Meter <-- Mass Moment of Inertia of Disc

(Calculation completed in 00.004 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 given Angular Velocity

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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 given Angular Velocity Formula

LaTeX Go

Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2)
I_d = q_r/(ω^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 given Angular Velocity?

Moment of Inertia of Disc given Angular Velocity calculator uses Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2) to calculate the Mass Moment of Inertia of Disc, Moment of Inertia of Disc given Angular Velocity formula is defined as a measure of an object's resistance to changes in its rotation, which is essential in understanding the behavior of rotating systems, particularly in the context of torsional vibrations. Mass Moment of Inertia of Disc is denoted by I_d symbol.

How to calculate Moment of Inertia of Disc given Angular Velocity using this online calculator? To use this online calculator for Moment of Inertia of Disc given Angular Velocity, enter Resistance Torsional Stiffness (q_r) & Angular Velocity (ω) and hit the calculate button. Here is how the Moment of Inertia of Disc given Angular Velocity calculation can be explained with given input values -> 6.2 = 777.728/(11.2^2).

FAQ

What is Moment of Inertia of Disc given Angular Velocity?

Moment of Inertia of Disc given Angular Velocity formula is defined as a measure of an object's resistance to changes in its rotation, which is essential in understanding the behavior of rotating systems, particularly in the context of torsional vibrations and is represented as I_d = q_r/(ω^2) or Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2). Resistance Torsional Stiffness is the resistance of an object to twisting or rotational deformation, measured by the amount of torque required to produce a unit of angular deformation & Angular Velocity is the measure of how quickly an object rotates or revolves around a central axis in a torsional vibration system.

How to calculate Moment of Inertia of Disc given Angular Velocity?

Moment of Inertia of Disc given Angular Velocity formula is defined as a measure of an object's resistance to changes in its rotation, which is essential in understanding the behavior of rotating systems, particularly in the context of torsional vibrations is calculated using Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2). To calculate Moment of Inertia of Disc given Angular Velocity, you need Resistance Torsional Stiffness (q_r) & Angular Velocity (ω). With our tool, you need to enter the respective value for Resistance Torsional Stiffness & Angular Velocity 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 Resistance Torsional Stiffness & Angular Velocity. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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