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Angular Velocity of Shaft Formula

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Angular Velocity is the measure of how quickly an object rotates or revolves around a central axis in a torsional vibration system. Check FAQs

ω = \sqrt{\frac{q r}{I d}}

ω - Angular Velocity?q_r - Resistance Torsional Stiffness?I_d - Mass Moment of Inertia of Disc?

Angular Velocity of Shaft Example

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Here is how the Angular Velocity of Shaft equation looks like with Values.

Here is how the Angular Velocity of Shaft equation looks like with Units.

Here is how the Angular Velocity of Shaft equation looks like.

11.2 = \sqrt{\frac{777.728}{6.2}}

11.2rad/s = \sqrt{\frac{777.728N/m}{6.2kg·m²}}

11.2 = \sqrt{\frac{777.728}{6.2}}

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Angular Velocity of Shaft Solution

Follow our step by step solution on how to calculate Angular Velocity of Shaft?

FIRST Step Consider the formula

ω = \sqrt{\frac{q r}{I d}}

Next Step Substitute values of Variables

∴

ω = \sqrt{\frac{777.728N/m}{6.2kg·m²}}

Next Step Prepare to Evaluate

∴

ω = \sqrt{\frac{777.728}{6.2}}

LAST Step Evaluate

∴

ω = 11.2rad/s

Angular Velocity of Shaft Formula Elements

Variables

Functions

Angular Velocity

Angular Velocity is the measure of how quickly an object rotates or revolves around a central axis in a torsional vibration system.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

Resistance Torsional Stiffness

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.

Symbol: q_r

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Resistance Torsional Stiffness

Mass Moment of Inertia of Disc

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.

Symbol: I_d

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Mass Moment of Inertia of Disc

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.

Syntax: sqrt(Number)

Other formulas in Natural Frequency of Free Torsional Vibrations category

Go Moment of Inertia of Disc using Natural Frequency of Vibration

I d = \frac{q}{{(2 \cdot π \cdot f n)}^{2}}

Go Torsional Stiffness of Shaft given Natural Frequency of Vibration

q = {(2 \cdot π \cdot f n)}^{2} \cdot I d

Go Moment of Inertia of Disc given Time Period of Vibration

I d = \frac{{t p}^{2} \cdot q}{{(2 \cdot π)}^{2}}

Go Torsional Stiffness of Shaft given Time Period of Vibration

q = \frac{{(2 \cdot π)}^{2} \cdot I d}{{(t p)}^{2}}

How to Evaluate Angular Velocity of Shaft?

Angular Velocity of Shaft evaluator uses Angular Velocity = sqrt(Resistance Torsional Stiffness/Mass Moment of Inertia of Disc) to evaluate 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 evaluate Angular Velocity of Shaft using this online evaluator? To use this online evaluator for Angular Velocity of Shaft, enter Resistance Torsional Stiffness (q_r) & Mass Moment of Inertia of Disc (I_d) and hit the calculate button.

FAQs on Angular Velocity of Shaft

What is the formula to find Angular Velocity of Shaft?

The formula of Angular Velocity of Shaft is expressed as Angular Velocity = sqrt(Resistance Torsional Stiffness/Mass Moment of Inertia of Disc). Here is an example- 11.2 = sqrt(777.728/6.2).

How to calculate Angular Velocity of Shaft?

With Resistance Torsional Stiffness (q_r) & Mass Moment of Inertia of Disc (I_d) we can find Angular Velocity of Shaft using the formula - Angular Velocity = sqrt(Resistance Torsional Stiffness/Mass Moment of Inertia of Disc). This formula also uses Square Root (sqrt) function(s).

Can the Angular Velocity of Shaft be negative?

No, the Angular Velocity of Shaft, measured in Angular Velocity cannot be negative.

Which unit is used to measure Angular Velocity of Shaft?

Angular Velocity of Shaft is usually measured using the Radian per Second[rad/s] for Angular Velocity. Radian per Day[rad/s], Radian per Hour[rad/s], Radian per Minute[rad/s] are the few other units in which Angular Velocity of Shaft can be measured.

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Angular Velocity of Shaft Formula

Angular Velocity of Shaft Example

Angular Velocity of Shaft Solution

Angular Velocity of Shaft Formula Elements

Other formulas in Natural Frequency of Free Torsional Vibrations category

How to Evaluate Angular Velocity of Shaft?

FAQs on Angular Velocity of Shaft

Variable Name