Angular Velocity of Element Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angular Velocity = (Angular Velocity of Free End*Distance between Small Element and Fixed End)/Length of Constraint
ω = (ωf*x)/l
This formula uses 4 Variables
Variables Used
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
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 Constraint - (Measured in Meter) - Length of Constraint is a measure of distance.
STEP 1: Convert Input(s) to Base Unit
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 Constraint: 7.33 Millimeter --> 0.00733 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ω = (ωf*x)/l --> (22.5*0.00366)/0.00733
Evaluating ... ...
ω = 11.2346521145975
STEP 3: Convert Result to Output's Unit
11.2346521145975 Radian per Second --> No Conversion Required
FINAL ANSWER
11.2346521145975 11.23465 Radian per Second <-- Angular Velocity
(Calculation completed in 00.020 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Verified by Dipto Mandal
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 Element Formula

Angular Velocity = (Angular Velocity of Free End*Distance between Small Element and Fixed End)/Length of Constraint
ω = (ωf*x)/l

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 Element?

Angular Velocity of Element calculator uses Angular Velocity = (Angular Velocity of Free End*Distance between Small Element and Fixed End)/Length of Constraint to calculate the Angular Velocity, Angular Velocity of Element is defined as a vector measure of the rotation rate, that refers to how fast an object rotates or revolves relative to another point. Angular Velocity is denoted by ω symbol.

How to calculate Angular Velocity of Element using this online calculator? To use this online calculator for Angular Velocity of Element, enter Angular Velocity of Free End f), Distance between Small Element and Fixed End (x) & Length of Constraint (l) and hit the calculate button. Here is how the Angular Velocity of Element calculation can be explained with given input values -> 3.245566 = (22.5*0.00366)/0.00733.

FAQ

What is Angular Velocity of Element?
Angular Velocity of Element is defined as a vector measure of the rotation rate, that refers to how fast an object rotates or revolves relative to another point and is represented as ω = (ωf*x)/l or Angular Velocity = (Angular Velocity of Free End*Distance between Small Element and Fixed End)/Length of Constraint. 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 Constraint is a measure of distance.
How to calculate Angular Velocity of Element?
Angular Velocity of Element is defined as a vector measure of the rotation rate, that refers to how fast an object rotates or revolves relative to another point is calculated using Angular Velocity = (Angular Velocity of Free End*Distance between Small Element and Fixed End)/Length of Constraint. To calculate Angular Velocity of Element, you need Angular Velocity of Free End f), Distance between Small Element and Fixed End (x) & Length of Constraint (l). With our tool, you need to enter the respective value for Angular Velocity of Free End, Distance between Small Element and Fixed End & Length of Constraint 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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