Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint Calculator

✖Kinetic Energy is the energy of an object due to its motion, particularly in the context of torsional vibrations, where it is related to the twisting motion.ⓘ Kinetic Energy [KE]			+10% -10%
✖Angular Velocity of Free End is the rotational speed of the free end of a torsional vibration system, measuring its oscillatory motion around a fixed axis.ⓘ Angular Velocity of Free End [ω_f]			+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 of Constraint given Kinetic Energy of Constraint [I_c]

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Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2)
I_c = (6*KE)/(ω_f^2)
This formula uses 3 Variables

Variables Used

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.
Kinetic Energy - (Measured in Joule) - Kinetic Energy is the energy of an object due to its motion, particularly in the context of torsional vibrations, where it is related to the twisting motion.
Angular Velocity of Free End - (Measured in Radian per Second) - Angular Velocity of Free End is the rotational speed of the free end of a torsional vibration system, measuring its oscillatory motion around a fixed axis.

STEP 1: Convert Input(s) to Base Unit

Kinetic Energy: 900 Joule --> 900 Joule No Conversion Required
Angular Velocity of Free End: 22.5176 Radian per Second --> 22.5176 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_c = (6*KE)/(ω_f^2) --> (6*900)/(22.5176^2)

Evaluating ... ...

I_c = 10.6499988187495

STEP 3: Convert Result to Output's Unit

10.6499988187495 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

10.6499988187495 ≈ 10.65 Kilogram Square Meter <-- Total Mass Moment of Inertia

(Calculation completed in 00.004 seconds)

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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

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint Formula

LaTeX Go

Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2)
I_c = (6*KE)/(ω_f^2)

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 Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint calculator uses Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2) to calculate the Total Mass Moment of Inertia, Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint formula is defined as a measure of the rotational inertia of an object undergoing torsional vibrations, which is a critical parameter in understanding the vibrational behavior of mechanical systems. Total Mass Moment of Inertia is denoted by I_c symbol.

How to calculate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint using this online calculator? To use this online calculator for Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint, enter Kinetic Energy (KE) & Angular Velocity of Free End (ω_f) and hit the calculate button. Here is how the Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint calculation can be explained with given input values -> 10.65 = (6*900)/(22.5176^2).

FAQ

What is Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint formula is defined as a measure of the rotational inertia of an object undergoing torsional vibrations, which is a critical parameter in understanding the vibrational behavior of mechanical systems and is represented as I_c = (6*KE)/(ω_f^2) or Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2). Kinetic Energy is the energy of an object due to its motion, particularly in the context of torsional vibrations, where it is related to the twisting motion & Angular Velocity of Free End is the rotational speed of the free end of a torsional vibration system, measuring its oscillatory motion around a fixed axis.

How to calculate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint formula is defined as a measure of the rotational inertia of an object undergoing torsional vibrations, which is a critical parameter in understanding the vibrational behavior of mechanical systems is calculated using Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2). To calculate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint, you need Kinetic Energy (KE) & Angular Velocity of Free End (ω_f). With our tool, you need to enter the respective value for Kinetic Energy & Angular Velocity of Free End 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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