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Moment of Inertia of Shaft given Circular Frequency Formula

GoMoment of Inertia of Shaft given Static Deflection given Load per Unit Length Formula

GoMoment of Inertia of Shaft given Natural Frequency Formula

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Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations. Check FAQs

I shaft = \frac{{ω n}^{2} \cdot w \cdot ({L shaft}^{4})}{π^{4} \cdot E \cdot g}

I_shaft - Moment of inertia of shaft?ω_n - Natural Circular Frequency?w - Load per unit length?L_shaft - Length of Shaft?E - Young's Modulus?g - Acceleration due to Gravity?π - Archimedes' constant?

Moment of Inertia of Shaft given Circular Frequency Example

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Here is how the Moment of Inertia of Shaft given Circular Frequency equation looks like with Values.

Here is how the Moment of Inertia of Shaft given Circular Frequency equation looks like with Units.

Here is how the Moment of Inertia of Shaft given Circular Frequency equation looks like.

5.3953 = \frac{{13.1}^{2} \cdot 3 \cdot ({3.5}^{4})}{{3.1416}^{4} \cdot 15 \cdot 9.8}

5.3953kg·m² = \frac{{13.1rad/s}^{2} \cdot 3 \cdot ({3.5m}^{4})}{{3.1416}^{4} \cdot 15N/m \cdot 9.8m/s²}

5.3953 = \frac{{13.1}^{2} \cdot 3 \cdot ({3.5}^{4})}{{3.1416}^{4} \cdot 15 \cdot 9.8}

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Moment of Inertia of Shaft given Circular Frequency Solution

Follow our step by step solution on how to calculate Moment of Inertia of Shaft given Circular Frequency?

FIRST Step Consider the formula

I shaft = \frac{{ω n}^{2} \cdot w \cdot ({L shaft}^{4})}{π^{4} \cdot E \cdot g}

Next Step Substitute values of Variables

∴

I shaft = \frac{{13.1rad/s}^{2} \cdot 3 \cdot ({3.5m}^{4})}{π^{4} \cdot 15N/m \cdot 9.8m/s²}

Next Step Substitute values of Constants

∴

I shaft = \frac{{13.1rad/s}^{2} \cdot 3 \cdot ({3.5m}^{4})}{{3.1416}^{4} \cdot 15N/m \cdot 9.8m/s²}

Next Step Prepare to Evaluate

∴

I shaft = \frac{{13.1}^{2} \cdot 3 \cdot ({3.5}^{4})}{{3.1416}^{4} \cdot 15 \cdot 9.8}

Next Step Evaluate

∴

I shaft = 5.39534472009954kg·m²

LAST Step Rounding Answer

∴

I shaft = 5.3953kg·m²

Moment of Inertia of Shaft given Circular Frequency Formula Elements

Variables

Constants

Moment of inertia of shaft

Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.

Symbol: I_shaft

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of inertia of shaft

Natural Circular Frequency

Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular Frequency

Load per unit length

Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.

Symbol: w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load per unit length

Length of Shaft

Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Young's Modulus

Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Acceleration due to Gravity

Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Moment of inertia of shaft

Go Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

I shaft = \frac{5 \cdot w \cdot {L shaft}^{4}}{384 \cdot E \cdot δ}

Go Moment of Inertia of Shaft given Natural Frequency

I shaft = \frac{4 \cdot f^{2} \cdot w \cdot {L shaft}^{4}}{π^{2} \cdot E \cdot g}

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

Go Circular Frequency given Static Deflection

ω n = 2 \cdot π \cdot \frac{0.5615}{\sqrt{δ}}

Go Natural Frequency given Static Deflection

f = \frac{0.5615}{\sqrt{δ}}

Go Uniformly Distributed Load Unit Length given Static Deflection

w = \frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot {L shaft}^{4}}

Go Length of Shaft given Static Deflection

L shaft = {(\frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot w})}^{\frac{1}{4}}

How to Evaluate Moment of Inertia of Shaft given Circular Frequency?

Moment of Inertia of Shaft given Circular Frequency evaluator uses Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity) to evaluate the Moment of inertia of shaft, Moment of Inertia of Shaft given Circular Frequency formula is defined as a measure of the shaft's resistance to changes in its rotational motion, which is essential in determining the natural frequency of free transverse vibrations in mechanical systems, particularly in the design of rotating machinery and structures. Moment of inertia of shaft is denoted by I_shaft symbol.

How to evaluate Moment of Inertia of Shaft given Circular Frequency using this online evaluator? To use this online evaluator for Moment of Inertia of Shaft given Circular Frequency, enter Natural Circular Frequency (ω_n), Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Acceleration due to Gravity (g) and hit the calculate button.

FAQs on Moment of Inertia of Shaft given Circular Frequency

What is the formula to find Moment of Inertia of Shaft given Circular Frequency?

The formula of Moment of Inertia of Shaft given Circular Frequency is expressed as Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity). Here is an example- 5.395345 = (13.1^2*3*(3.5^4))/(pi^4*15*9.8).

How to calculate Moment of Inertia of Shaft given Circular Frequency?

With Natural Circular Frequency (ω_n), Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Acceleration due to Gravity (g) we can find Moment of Inertia of Shaft given Circular Frequency using the formula - Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity). This formula also uses Archimedes' constant .

What are the other ways to Calculate Moment of inertia of shaft?

Here are the different ways to Calculate Moment of inertia of shaft-

Moment of inertia of shaft=(5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
Moment of inertia of shaft=(4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity)

Can the Moment of Inertia of Shaft given Circular Frequency be negative?

No, the Moment of Inertia of Shaft given Circular Frequency, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Moment of Inertia of Shaft given Circular Frequency?

Moment of Inertia of Shaft given Circular Frequency is usually measured using the Kilogram Square Meter[kg·m²] for Moment of Inertia. Kilogram Square Centimeter[kg·m²], Kilogram Square Millimeter[kg·m²], Gram Square Centimeter[kg·m²] are the few other units in which Moment of Inertia of Shaft given Circular Frequency can be measured.

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Moment of Inertia of Shaft given Circular Frequency Formula

​GoMoment of Inertia of Shaft given Static Deflection given Load per Unit Length Formula

​GoMoment of Inertia of Shaft given Natural Frequency Formula

Moment of Inertia of Shaft given Circular Frequency Example

Moment of Inertia of Shaft given Circular Frequency Solution

Moment of Inertia of Shaft given Circular Frequency Formula Elements

Other Formulas to find Moment of inertia of shaft

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

How to Evaluate Moment of Inertia of Shaft given Circular Frequency?

FAQs on Moment of Inertia of Shaft given Circular Frequency

Variable Name

GoMoment of Inertia of Shaft given Static Deflection given Load per Unit Length Formula

GoMoment of Inertia of Shaft given Natural Frequency Formula