Mass Moment of Inertia of Element Calculator

✖Length of Small Element is the distance of a small portion of a shaft in torsional vibrations, used to calculate the angular displacement of the shaft.ⓘ Length of Small Element [δ_x]			+10% -10%
✖Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system.ⓘ Total Mass Moment of Inertia [I_c]			+10% -10%
✖Length of Constraint is the distance between the point of application of the torsional load and the axis of rotation of the shaft.ⓘ Length of Constraint [l]			+10% -10%

✖Moment of Inertia is a measure of an object's resistance to changes in its rotation, influencing the vibrational behavior in torsional vibrations.ⓘ Mass Moment of Inertia of Element [I]

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Mass Moment of Inertia of Element Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint
I = (δ_x*I_c)/l
This formula uses 4 Variables

Variables Used

Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is a measure of an object's resistance to changes in its rotation, influencing the vibrational behavior in torsional vibrations.
Length of Small Element - (Measured in Meter) - Length of Small Element is the distance of a small portion of a shaft in torsional vibrations, used to calculate the angular displacement of the shaft.
Total Mass Moment of Inertia - (Measured in Kilogram Square Meter) - Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system.
Length of Constraint - (Measured in Meter) - Length of Constraint is the distance between the point of application of the torsional load and the axis of rotation of the shaft.

STEP 1: Convert Input(s) to Base Unit

Length of Small Element: 9.82 Millimeter --> 0.00982 Meter (Check conversion here)
Total Mass Moment of Inertia: 10.65 Kilogram Square Meter --> 10.65 Kilogram Square Meter No Conversion Required
Length of Constraint: 7.33 Millimeter --> 0.00733 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (δ_x*I_c)/l --> (0.00982*10.65)/0.00733

Evaluating ... ...

I = 14.2678035470669

STEP 3: Convert Result to Output's Unit

14.2678035470669 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

14.2678035470669 ≈ 14.2678 Kilogram Square Meter <-- Moment of Inertia

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Mechanical » Effect of Inertia of Constraint on Torsional Vibrations » Mass Moment of Inertia of Element

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Effect of Inertia of Constraint on Torsional Vibrations Calculators

Kinetic Energy Possessed by Element

LaTeX Go Kinetic Energy = (Total Mass Moment of Inertia*(Angular Velocity of Free End*Distance Between Small Element and Fixed End)^2*Length of Small Element)/(2*Length of Constraint^3)

Angular Velocity of Element

LaTeX Go Angular Velocity = (Angular Velocity of Free End*Distance Between Small Element and Fixed End)/Length of Constraint

Mass Moment of Inertia of Element

LaTeX Go Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint

Total Kinetic Energy of Constraint

LaTeX Go Kinetic Energy = (Total Mass Moment of Inertia*Angular Velocity of Free End^2)/6

Mass Moment of Inertia of Element Formula

LaTeX Go

Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint
I = (δ_x*I_c)/l

What causes torsional vibration on the shaft?

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 Mass Moment of Inertia of Element?

Mass Moment of Inertia of Element calculator uses Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint to calculate the Moment of Inertia, Mass Moment of Inertia of Element formula is defined as a measure of the tendency of an object to resist changes in its rotational motion, which is crucial in understanding the behavior of objects in torsional vibrations, particularly in mechanical systems where rotational motion is involved. Moment of Inertia is denoted by I symbol.

How to calculate Mass Moment of Inertia of Element using this online calculator? To use this online calculator for Mass Moment of Inertia of Element, enter Length of Small Element (δ_x), Total Mass Moment of Inertia (I_c) & Length of Constraint (l) and hit the calculate button. Here is how the Mass Moment of Inertia of Element calculation can be explained with given input values -> 14.2678 = (0.00982*10.65)/0.00733.

FAQ

What is Mass Moment of Inertia of Element?

Mass Moment of Inertia of Element formula is defined as a measure of the tendency of an object to resist changes in its rotational motion, which is crucial in understanding the behavior of objects in torsional vibrations, particularly in mechanical systems where rotational motion is involved and is represented as I = (δ_x*I_c)/l or Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint. Length of Small Element is the distance of a small portion of a shaft in torsional vibrations, used to calculate the angular displacement of the shaft, Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system & Length of Constraint is the distance between the point of application of the torsional load and the axis of rotation of the shaft.

How to calculate Mass Moment of Inertia of Element?

Mass Moment of Inertia of Element formula is defined as a measure of the tendency of an object to resist changes in its rotational motion, which is crucial in understanding the behavior of objects in torsional vibrations, particularly in mechanical systems where rotational motion is involved is calculated using Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint. To calculate Mass Moment of Inertia of Element, you need Length of Small Element (δ_x), Total Mass Moment of Inertia (I_c) & Length of Constraint (l). With our tool, you need to enter the respective value for Length of Small Element, Total Mass Moment of Inertia & Length of Constraint 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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