Angular Velocity of Shaft Calculator

✖Resistance Torsional Stiffness is the resistance of an object to twisting or rotational deformation, measured by the amount of torque required to produce a unit of angular deformation.ⓘ Resistance Torsional Stiffness [q_r]			+10% -10%
✖Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.ⓘ Mass Moment of Inertia of Disc [I_d]			+10% -10%

✖Angular Velocity is the measure of how quickly an object rotates or revolves around a central axis in a torsional vibration system.ⓘ Angular Velocity of Shaft [ω]

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Angular Velocity of Shaft Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Velocity = sqrt(Resistance Torsional Stiffness/Mass Moment of Inertia of Disc)
ω = sqrt(q_r/I_d)
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) - Angular Velocity is the measure of how quickly an object rotates or revolves around a central axis in a torsional vibration system.
Resistance Torsional Stiffness - (Measured in Newton per Meter) - Resistance Torsional Stiffness is the resistance of an object to twisting or rotational deformation, measured by the amount of torque required to produce a unit of angular deformation.
Mass Moment of Inertia of Disc - (Measured in Kilogram Square Meter) - Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.

STEP 1: Convert Input(s) to Base Unit

Resistance Torsional Stiffness: 777.728 Newton per Meter --> 777.728 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(q_r/I_d) --> sqrt(777.728/6.2)

Evaluating ... ...

ω = 11.2

STEP 3: Convert Result to Output's Unit

11.2 Radian per Second --> No Conversion Required

FINAL ANSWER

11.2 Radian per Second <-- Angular Velocity

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Mechanical » Natural Frequency of Free Torsional Vibrations » Angular Velocity of Shaft

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Natural Frequency of Free Torsional Vibrations Calculators

Moment of Inertia of Disc using Natural Frequency of Vibration

LaTeX Go Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2)

Torsional Stiffness of Shaft given Natural Frequency of Vibration

LaTeX Go Torsional Stiffness = (2*pi*Natural Frequency)^2*Mass Moment of Inertia of Disc

Torsional Stiffness of Shaft given Time Period of Vibration

LaTeX 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

LaTeX Go Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)

Angular Velocity of Shaft Formula

LaTeX Go

Angular Velocity = sqrt(Resistance Torsional Stiffness/Mass Moment of Inertia of Disc)
ω = sqrt(q_r/I_d)

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(Resistance Torsional Stiffness/Mass Moment of Inertia of Disc) to calculate the Angular Velocity, Angular Velocity of Shaft formula is defined as a measure of the rotational speed of a shaft in a mechanical system, typically used to analyze and understand the torsional vibrations and oscillations in rotating machinery. 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 Resistance Torsional Stiffness (q_r) & Mass Moment of Inertia of Disc (I_d) and hit the calculate button. Here is how the Angular Velocity of Shaft calculation can be explained with given input values -> 11.2 = sqrt(777.728/6.2).

FAQ

What is Angular Velocity of Shaft?

Angular Velocity of Shaft formula is defined as a measure of the rotational speed of a shaft in a mechanical system, typically used to analyze and understand the torsional vibrations and oscillations in rotating machinery and is represented as ω = sqrt(q_r/I_d) or Angular Velocity = sqrt(Resistance Torsional Stiffness/Mass Moment of Inertia of Disc). Resistance Torsional Stiffness is the resistance of an object to twisting or rotational deformation, measured by the amount of torque required to produce a unit of angular deformation & Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.

How to calculate Angular Velocity of Shaft?

Angular Velocity of Shaft formula is defined as a measure of the rotational speed of a shaft in a mechanical system, typically used to analyze and understand the torsional vibrations and oscillations in rotating machinery is calculated using Angular Velocity = sqrt(Resistance Torsional Stiffness/Mass Moment of Inertia of Disc). To calculate Angular Velocity of Shaft, you need Resistance Torsional Stiffness (q_r) & Mass Moment of Inertia of Disc (I_d). With our tool, you need to enter the respective value for Resistance Torsional Stiffness & 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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