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Natural Circular Frequency of Shaft Formula

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Natural Circular Frequency is a scalar measure of rotation rate. Check FAQs

ω n = \sqrt{\frac{S s}{m}}

ω_n - Natural Circular Frequency?S_s - Stiffness of Shaft?m - Mass of Rotor?

Natural Circular Frequency of Shaft Example

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Here is how the Natural Circular Frequency of Shaft equation looks like with Values.

Here is how the Natural Circular Frequency of Shaft equation looks like with Units.

Here is how the Natural Circular Frequency of Shaft equation looks like.

67.8233 = \sqrt{\frac{2.3}{0.0005}}

67.8233rad/s = \sqrt{\frac{2.3N/m}{0.0005kg}}

67.8233 = \sqrt{\frac{2.3}{0.0005}}

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Natural Circular Frequency of Shaft Solution

Follow our step by step solution on how to calculate Natural Circular Frequency of Shaft?

FIRST Step Consider the formula

ω n = \sqrt{\frac{S s}{m}}

Next Step Substitute values of Variables

∴

ω n = \sqrt{\frac{2.3N/m}{0.0005kg}}

Next Step Prepare to Evaluate

∴

ω n = \sqrt{\frac{2.3}{0.0005}}

Next Step Evaluate

∴

ω n = 67.8232998312527rad/s

LAST Step Rounding Answer

∴

ω n = 67.8233rad/s

Natural Circular Frequency of Shaft Formula Elements

Variables

Functions

Natural Circular Frequency

Natural Circular Frequency is a scalar measure of rotation rate.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular Frequency

Stiffness of Shaft

Stiffness of Shaft means that the lateral deflection of the shaft and/or angle of twist of the shaft should be within some prescribed limit.

Symbol: S_s

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Stiffness of Shaft

Mass of Rotor

Mass of Rotor is both a property of a physical body and a measure of its resistance to acceleration.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Rotor

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 Critical or Whirling Speed of Shaft category

Go Static Deflection of Shaft

δ = \frac{m \cdot g}{S s}

Go Critical or Whirling Speed in R.P.S

ω c = \frac{0.4985}{\sqrt{δ}}

Go Critical or Whirling Speed given Static Deflection

ω c = \sqrt{\frac{g}{δ}}

Go Critical or Whirling Speed given Stiffness of Shaft

ω c = \sqrt{\frac{S s}{m}}

How to Evaluate Natural Circular Frequency of Shaft?

Natural Circular Frequency of Shaft evaluator uses Natural Circular Frequency = sqrt(Stiffness of Shaft/Mass of Rotor) to evaluate the Natural Circular Frequency, Natural Circular Frequency of Shaft formula is defined as a measure of the shaft's tendency to vibrate at a specific frequency when subjected to external forces, critical to determining the whirling speed of a shaft in rotating machinery, ensuring stable operation and preventing damage. Natural Circular Frequency is denoted by ω_n symbol.

How to evaluate Natural Circular Frequency of Shaft using this online evaluator? To use this online evaluator for Natural Circular Frequency of Shaft, enter Stiffness of Shaft (S_s) & Mass of Rotor (m) and hit the calculate button.

FAQs on Natural Circular Frequency of Shaft

What is the formula to find Natural Circular Frequency of Shaft?

The formula of Natural Circular Frequency of Shaft is expressed as Natural Circular Frequency = sqrt(Stiffness of Shaft/Mass of Rotor). Here is an example- 67.8233 = sqrt(2.3/0.0005).

How to calculate Natural Circular Frequency of Shaft?

With Stiffness of Shaft (S_s) & Mass of Rotor (m) we can find Natural Circular Frequency of Shaft using the formula - Natural Circular Frequency = sqrt(Stiffness of Shaft/Mass of Rotor). This formula also uses Square Root (sqrt) function(s).

Can the Natural Circular Frequency of Shaft be negative?

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

Which unit is used to measure Natural Circular Frequency of Shaft?

Natural Circular Frequency 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 Natural Circular Frequency of Shaft can be measured.

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Natural Circular Frequency of Shaft Formula

Natural Circular Frequency of Shaft Example

Natural Circular Frequency of Shaft Solution

Natural Circular Frequency of Shaft Formula Elements

Other formulas in Critical or Whirling Speed of Shaft category

How to Evaluate Natural Circular Frequency of Shaft?

FAQs on Natural Circular Frequency of Shaft

Variable Name