Angular Velocity of Shaft Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angular Velocity = sqrt(Torsional Stiffness of Shaft/Mass Moment of Inertia of Disc)
ω = sqrt(qshaft/Idisc)
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 - (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.
Torsional Stiffness of Shaft - (Measured in Newton per Meter) - Torsional Stiffness of Shaft is the measurement of how much a given diameter of shaft bends under load.
Mass Moment of Inertia of Disc - (Measured in Kilogram Square Meter) - Mass moment of inertia of disc is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.
STEP 1: Convert Input(s) to Base Unit
Torsional Stiffness of Shaft: 777 Newton per Meter --> 777 Newton per Meter No Conversion Required
Mass Moment of Inertia of Disc: 6.2 Kilogram Square Meter --> 6.2 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ω = sqrt(qshaft/Idisc) --> sqrt(777/6.2)
Evaluating ... ...
ω = 11.1947568372503
STEP 3: Convert Result to Output's Unit
11.1947568372503 Radian per Second --> No Conversion Required
FINAL ANSWER
11.1947568372503 11.19476 Radian per Second <-- Angular Velocity
(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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13 Natural Frequency of Free Torsional Vibrations Calculators

Natural Frequency of Vibration
Go Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi)
Time Period for Vibrations
Go Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness)
Angular Velocity of Shaft
Go Angular Velocity = sqrt(Torsional Stiffness of Shaft/Mass Moment of Inertia of Disc)
Torsional Stiffness of Shaft given Time Period of Vibration
Go Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2
Moment of Inertia of Disc given Time Period of Vibration
Go Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)
Moment of Inertia of Disc using Natural Frequency of Vibration
Go Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Frequency)^2)
Torsional Stiffness of Shaft given Natural Frequency of Vibration
Go Torsional Stiffness = (2*pi*Frequency)^2*Mass Moment of Inertia of Disc
Moment of Inertia of Disc given Angular Velocity
Go Mass Moment of Inertia of Disc = Torsional Stiffness of Shaft/(Angular Velocity^2)
Torsional Stiffness of Shaft given Angular Velocity
Go Torsional Stiffness of Shaft = Angular Velocity^2*Mass Moment of Inertia of Disc
Angular Displacement of Shaft from Mean Position
Go Angular Displacement of Shaft = Restoring Force/Torsional Stiffness
Restoring Force for Free Torsional Vibrations
Go Restoring Force = Torsional Stiffness*Angular Displacement of Shaft
Torsional Stiffness of Shaft
Go Torsional Stiffness = Restoring Force/Angular Displacement of Shaft
Accelerating Force
Go Force = Mass Moment of Inertia of Disc*Angular Acceleration

Angular Velocity of Shaft Formula

Angular Velocity = sqrt(Torsional Stiffness of Shaft/Mass Moment of Inertia of Disc)
ω = sqrt(qshaft/Idisc)

What causes torsional vibration?

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 Shaft?

Angular Velocity of Shaft calculator uses Angular Velocity = sqrt(Torsional Stiffness of Shaft/Mass Moment of Inertia of Disc) to calculate the Angular Velocity, The Angular velocity of shaft formula 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 Shaft using this online calculator? To use this online calculator for Angular Velocity of Shaft, enter Torsional Stiffness of Shaft (qshaft) & Mass Moment of Inertia of Disc (Idisc) and hit the calculate button. Here is how the Angular Velocity of Shaft calculation can be explained with given input values -> 0.933257 = sqrt(777/6.2).

FAQ

What is Angular Velocity of Shaft?
The Angular velocity of shaft formula 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 = sqrt(qshaft/Idisc) or Angular Velocity = sqrt(Torsional Stiffness of Shaft/Mass Moment of Inertia of Disc). Torsional Stiffness of Shaft is the measurement of how much a given diameter of shaft bends under load & Mass moment of inertia of disc is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.
How to calculate Angular Velocity of Shaft?
The Angular velocity of shaft formula 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 = sqrt(Torsional Stiffness of Shaft/Mass Moment of Inertia of Disc). To calculate Angular Velocity of Shaft, you need Torsional Stiffness of Shaft (qshaft) & Mass Moment of Inertia of Disc (Idisc). With our tool, you need to enter the respective value for Torsional Stiffness of Shaft & Mass Moment of Inertia of Disc 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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