Angular Velocity of Free End using 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%
✖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%

✖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 using Kinetic Energy of Constraint [ω_f]

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Angular Velocity of Free End using Kinetic Energy of Constraint Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass Moment of Inertia)
ω_f = sqrt((6*KE)/I_c)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Kinetic Energy: 900 Joule --> 900 Joule No Conversion Required
Total Mass Moment of Inertia: 10.65 Kilogram Square Meter --> 10.65 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_f = sqrt((6*KE)/I_c) --> sqrt((6*900)/10.65)

Evaluating ... ...

ω_f = 22.517598751224

STEP 3: Convert Result to Output's Unit

22.517598751224 Radian per Second --> No Conversion Required

FINAL ANSWER

22.517598751224 ≈ 22.5176 Radian per Second <-- Angular Velocity of Free End

(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 » Angular Velocity of Free End using Kinetic Energy of Constraint

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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

Angular Velocity of Free End using Kinetic Energy of Constraint Formula

LaTeX Go

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

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 Angular Velocity of Free End using Kinetic Energy of Constraint?

Angular Velocity of Free End using Kinetic Energy of Constraint calculator uses Angular Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass Moment of Inertia) to calculate the Angular Velocity of Free End, Angular Velocity of Free End using Kinetic Energy of Constraint formula is defined as a measure of the rotational speed of a free end in a torsional vibration system, which is influenced by the kinetic energy of the constraint and the moment of inertia of the system. Angular Velocity of Free End is denoted by ω_f symbol.

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

FAQ

What is Angular Velocity of Free End using Kinetic Energy of Constraint?

Angular Velocity of Free End using Kinetic Energy of Constraint formula is defined as a measure of the rotational speed of a free end in a torsional vibration system, which is influenced by the kinetic energy of the constraint and the moment of inertia of the system and is represented as ω_f = sqrt((6*KE)/I_c) or Angular Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass Moment of Inertia). 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 & Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system.

How to calculate Angular Velocity of Free End using Kinetic Energy of Constraint?

Angular Velocity of Free End using Kinetic Energy of Constraint formula is defined as a measure of the rotational speed of a free end in a torsional vibration system, which is influenced by the kinetic energy of the constraint and the moment of inertia of the system is calculated using Angular Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass Moment of Inertia). To calculate Angular Velocity of Free End using Kinetic Energy of Constraint, you need Kinetic Energy (KE) & Total Mass Moment of Inertia (I_c). With our tool, you need to enter the respective value for Kinetic Energy & Total Mass Moment of Inertia 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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