Total Kinetic Energy of Constraint Calculator

✖Total Mass Moment of Inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analog to mass.ⓘ Total Mass Moment of Inertia [I_c]			+10% -10%
✖Angular Velocity of Free End is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.ⓘ Angular Velocity of Free End [ω_f]			+10% -10%

✖Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.ⓘ Total Kinetic Energy of Constraint [KE]

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Formula

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Total Kinetic Energy of Constraint

Formula

`"KE" = ("I"_{"c"}*"ω"_{"f"}^2)/6`

Example

`"898.5938J"=("10.65kg·m²"*("22.5rad/s")^2)/6`

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Total Kinetic Energy of Constraint Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Kinetic Energy - (Measured in Joule) - Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Total Mass Moment of Inertia - (Measured in Kilogram Square Meter) - Total Mass Moment of Inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analog to mass.
Angular Velocity of Free End - (Measured in Radian per Second) - Angular Velocity of Free End is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.

STEP 1: Convert Input(s) to Base Unit

Total Mass Moment of Inertia: 10.65 Kilogram Square Meter --> 10.65 Kilogram Square Meter No Conversion Required
Angular Velocity of Free End: 22.5 Radian per Second --> 22.5 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

KE = (I_c*ω_f^2)/6 --> (10.65*22.5^2)/6

Evaluating ... ...

KE = 898.59375

STEP 3: Convert Result to Output's Unit

898.59375 Joule --> No Conversion Required

FINAL ANSWER

898.59375 ≈ 898.5938 Joule <-- Kinetic Energy

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Effect of Inertia of Constraint on Torsional Vibrations » Total Kinetic Energy of Constraint

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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< 8 Effect of Inertia of Constraint on Torsional Vibrations Calculators

Kinetic Energy Possessed by Element

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)

Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint

Go Frequency = (sqrt(Torsional Stiffness/(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)))/(2*pi)

Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations

Go Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)

Angular Velocity of Element

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

Mass Moment of Inertia of Element

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

Angular Velocity of Free End using Kinetic Energy of Constraint

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

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

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

Total Kinetic Energy of Constraint

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

Total Kinetic Energy of Constraint Formula

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

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 Kinetic Energy of Constraint?

Total Kinetic Energy of Constraint calculator uses Kinetic Energy = (Total Mass Moment of Inertia*Angular Velocity of Free End^2)/6 to calculate the Kinetic Energy, The Total kinetic energy of constraint formula is defined as a property of a moving object or particle and depends not only on its motion but also on its mass. Kinetic Energy is denoted by KE symbol.

How to calculate Total Kinetic Energy of Constraint using this online calculator? To use this online calculator for Total Kinetic Energy of Constraint, enter Total Mass Moment of Inertia (I_c) & Angular Velocity of Free End (ω_f) and hit the calculate button. Here is how the Total Kinetic Energy of Constraint calculation can be explained with given input values -> 898.5938 = (10.65*22.5^2)/6.

FAQ

What is Total Kinetic Energy of Constraint?

The Total kinetic energy of constraint formula is defined as a property of a moving object or particle and depends not only on its motion but also on its mass and is represented as KE = (I_c*ω_f^2)/6 or Kinetic Energy = (Total Mass Moment of Inertia*Angular Velocity of Free End^2)/6. Total Mass Moment of Inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analog to mass & Angular Velocity of Free End is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.

How to calculate Total Kinetic Energy of Constraint?

The Total kinetic energy of constraint formula is defined as a property of a moving object or particle and depends not only on its motion but also on its mass is calculated using Kinetic Energy = (Total Mass Moment of Inertia*Angular Velocity of Free End^2)/6. To calculate Total Kinetic Energy of Constraint, you need Total Mass Moment of Inertia (I_c) & Angular Velocity of Free End (ω_f). With our tool, you need to enter the respective value for Total Mass Moment of Inertia & 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.

How many ways are there to calculate Kinetic Energy?

In this formula, Kinetic Energy uses Total Mass Moment of Inertia & Angular Velocity of Free End. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)

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