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M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Formula

GoM.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load Formula

GoM.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) 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{f^{2} \cdot w \cdot {L shaft}^{4}}{{3.573}^{2} \cdot E \cdot g}

I_shaft - Moment of inertia of shaft?f - Frequency?w - Load per unit length?L_shaft - Length of Shaft?E - Young's Modulus?g - Acceleration due to Gravity?

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Example

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Here is how the M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load equation looks like with Values.

Here is how the M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load equation looks like with Units.

Here is how the M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load equation looks like.

1943.0997 = \frac{90^{2} \cdot 3 \cdot {3.5}^{4}}{{3.573}^{2} \cdot 15 \cdot 9.8}

1943.0997kg·m² = \frac{{90Hz}^{2} \cdot 3 \cdot {3.5m}^{4}}{{3.573}^{2} \cdot 15N/m \cdot 9.8m/s²}

1943.0997 = \frac{90^{2} \cdot 3 \cdot {3.5}^{4}}{{3.573}^{2} \cdot 15 \cdot 9.8}

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M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Solution

Follow our step by step solution on how to calculate M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?

FIRST Step Consider the formula

I shaft = \frac{f^{2} \cdot w \cdot {L shaft}^{4}}{{3.573}^{2} \cdot E \cdot g}

Next Step Substitute values of Variables

∴

I shaft = \frac{{90Hz}^{2} \cdot 3 \cdot {3.5m}^{4}}{{3.573}^{2} \cdot 15N/m \cdot 9.8m/s²}

Next Step Prepare to Evaluate

∴

I shaft = \frac{90^{2} \cdot 3 \cdot {3.5}^{4}}{{3.573}^{2} \cdot 15 \cdot 9.8}

Next Step Evaluate

∴

I shaft = 1943.09969608335kg·m²

LAST Step Rounding Answer

∴

I shaft = 1943.0997kg·m²

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Formula Elements

Variables

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

Frequency

Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find 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

Other Formulas to find Moment of inertia of shaft

Go M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load

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

Go M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

I shaft = \frac{{ω n}^{2} \cdot w \cdot {L shaft}^{4}}{504 \cdot E \cdot g}

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

Go Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

ω n = \frac{2 \cdot π \cdot 0.571}{\sqrt{δ}}

Go Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

δ = {(\frac{0.571}{f})}^{2}

Go Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

f = \frac{0.571}{\sqrt{δ}}

Go Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

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

How to Evaluate M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load evaluator uses Moment of inertia of shaft = (Frequency^2*Load per unit length*Length of Shaft^4)/(3.573^2*Young's Modulus*Acceleration due to Gravity) to evaluate the Moment of inertia of shaft, M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load formula is defined as a measure of the moment of inertia of a shaft under fixed support conditions with a uniformly distributed load, which is essential in determining the natural frequency of free transverse vibrations in mechanical systems. Moment of inertia of shaft is denoted by I_shaft symbol.

How to evaluate M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load using this online evaluator? To use this online evaluator for M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load, enter Frequency (f), 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 M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load

What is the formula to find M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?

The formula of M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load is expressed as Moment of inertia of shaft = (Frequency^2*Load per unit length*Length of Shaft^4)/(3.573^2*Young's Modulus*Acceleration due to Gravity). Here is an example- 1943.1 = (90^2*3*3.5^4)/(3.573^2*15*9.8).

How to calculate M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?

With Frequency (f), Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Acceleration due to Gravity (g) we can find M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load using the formula - Moment of inertia of shaft = (Frequency^2*Load per unit length*Length of Shaft^4)/(3.573^2*Young's Modulus*Acceleration due to Gravity).

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=(Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
Moment of inertia of shaft=(Natural Circular Frequency^2*Load per unit length*Length of Shaft^4)/(504*Young's Modulus*Acceleration due to Gravity)

Can the M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load be negative?

No, the M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load, measured in Moment of Inertia cannot be negative.

Which unit is used to measure M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load 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 M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load can be measured.

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M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Formula

​GoM.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load Formula

​GoM.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Formula

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Example

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Solution

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load Formula Elements

Other Formulas to find Moment of inertia of shaft

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

How to Evaluate M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load?

FAQs on M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load

Variable Name

GoM.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load Formula

GoM.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) Formula