Kinetic Energy Possessed by Element Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
KE = (Ic*(ωf*x)^2*δx)/(2*l^3)
This formula uses 6 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.
Distance between Small Element and Fixed End - (Measured in Meter) - Distance between Small Element and Fixed End is a numerical measurement of how far apart objects or points are.
Length of Small Element - (Measured in Meter) - Length of Small Element is a measure of distance.
Length of Constraint - (Measured in Meter) - Length of Constraint is a measure of distance.
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
Distance between Small Element and Fixed End: 3.66 Millimeter --> 0.00366 Meter (Check conversion here)
Length of Small Element: 9.82 Millimeter --> 0.00982 Meter (Check conversion here)
Length of Constraint: 7.33 Millimeter --> 0.00733 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
KE = (Ic*(ωf*x)^2*δx)/(2*l^3) --> (10.65*(22.5*0.00366)^2*0.00982)/(2*0.00733^3)
Evaluating ... ...
KE = 900.422591752425
STEP 3: Convert Result to Output's Unit
900.422591752425 Joule --> No Conversion Required
FINAL ANSWER
900.422591752425 900.4226 Joule <-- Kinetic Energy
(Calculation completed in 00.004 seconds)

Credits

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

Kinetic Energy Possessed by Element Formula

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)
KE = (Ic*(ωf*x)^2*δx)/(2*l^3)

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 Kinetic Energy Possessed by Element?

Kinetic Energy Possessed by Element calculator uses 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) to calculate the Kinetic Energy, Kinetic Energy Possessed by Element 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 Kinetic Energy Possessed by Element using this online calculator? To use this online calculator for Kinetic Energy Possessed by Element, enter Total Mass Moment of Inertia (Ic), Angular Velocity of Free End f), Distance between Small Element and Fixed End (x), Length of Small Element (δx) & Length of Constraint (l) and hit the calculate button. Here is how the Kinetic Energy Possessed by Element calculation can be explained with given input values -> 900.4226 = (10.65*(22.5*0.00366)^2*0.00982)/(2*0.00733^3).

FAQ

What is Kinetic Energy Possessed by Element?
Kinetic Energy Possessed by Element 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 = (Ic*(ωf*x)^2*δx)/(2*l^3) or 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). 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, Distance between Small Element and Fixed End is a numerical measurement of how far apart objects or points are, Length of Small Element is a measure of distance & Length of Constraint is a measure of distance.
How to calculate Kinetic Energy Possessed by Element?
Kinetic Energy Possessed by Element 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*Distance between Small Element and Fixed End)^2*Length of Small Element)/(2*Length of Constraint^3). To calculate Kinetic Energy Possessed by Element, you need Total Mass Moment of Inertia (Ic), Angular Velocity of Free End f), Distance between Small Element and Fixed End (x), Length of Small Element (δx) & Length of Constraint (l). With our tool, you need to enter the respective value for Total Mass Moment of Inertia, Angular Velocity of Free End, Distance between Small Element and Fixed End, Length of Small Element & Length of Constraint 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, Distance between Small Element and Fixed End, Length of Small Element & Length of Constraint. 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^2)/6
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