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)
ωf = sqrt((6*KE)/Ic)
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 a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.
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.
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
ωf = sqrt((6*KE)/Ic) --> sqrt((6*900)/10.65)
Evaluating ... ...
ωf = 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 00.004 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

Angular Velocity of Free End using Kinetic Energy of Constraint Formula

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

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 is defined as a vector measure of the rotation rate, which refers to how fast an object rotates or revolves relative to another point. Angular Velocity of Free End is denoted by ωf 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 (Ic) 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 is defined as a vector measure of the rotation rate, which refers to how fast an object rotates or revolves relative to another point and is represented as ωf = sqrt((6*KE)/Ic) or Angular Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass Moment of Inertia). 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 measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analog to mass.
How to calculate Angular Velocity of Free End using Kinetic Energy of Constraint?
Angular Velocity of Free End using Kinetic Energy of Constraint is defined as a vector measure of the rotation rate, which refers to how fast an object rotates or revolves relative to another point 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 (Ic). 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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