FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

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

GoMoment of Inertia of Shaft given Natural Frequency Formula

GoMoment of Inertia of Shaft given Circular Frequency Formula

Fx Copy

LaTeX Copy

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

I_shaft - Moment of inertia of shaft?w - Load per unit length?L_shaft - Length of Shaft?E - Young's Modulus?δ - Static Deflection?

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

With values

With units

Only example

Here is how the Moment of Inertia of Shaft given Static Deflection given Load per Unit Length equation looks like with Values.

Here is how the Moment of Inertia of Shaft given Static Deflection given Load per Unit Length equation looks like with Units.

Here is how the Moment of Inertia of Shaft given Static Deflection given Load per Unit Length equation looks like.

5.4276 = \frac{5 \cdot 3 \cdot {3.5}^{4}}{384 \cdot 15 \cdot 0.072}

5.4276kg·m² = \frac{5 \cdot 3 \cdot {3.5m}^{4}}{384 \cdot 15N/m \cdot 0.072m}

5.4276 = \frac{5 \cdot 3 \cdot {3.5}^{4}}{384 \cdot 15 \cdot 0.072}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Machine » fx Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

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

Follow our step by step solution on how to calculate Moment of Inertia of Shaft given Static Deflection given Load per Unit Length?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I shaft = \frac{5 \cdot 3 \cdot {3.5m}^{4}}{384 \cdot 15N/m \cdot 0.072m}

Next Step Prepare to Evaluate

∴

I shaft = \frac{5 \cdot 3 \cdot {3.5}^{4}}{384 \cdot 15 \cdot 0.072}

Next Step Evaluate

∴

I shaft = 5.42760778356481kg·m²

LAST Step Rounding Answer

∴

I shaft = 5.4276kg·m²

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

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

Static Deflection

Static Deflection is the maximum displacement of an object from its equilibrium position during free transverse vibrations, indicating its flexibility and stiffness.

Symbol: δ

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Static Deflection

Other Formulas to find Moment of inertia of shaft

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}

Go Moment of Inertia of Shaft given Circular Frequency

I shaft = \frac{{ω n}^{2} \cdot w \cdot ({L shaft}^{4})}{π^{4} \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 Static Deflection given Load per Unit Length?

Moment of Inertia of Shaft given Static Deflection given Load per Unit Length evaluator uses Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection) to evaluate the Moment of inertia of shaft, Moment of Inertia of Shaft given Static Deflection given Load per Unit Length formula is defined as a measure of an object's resistance to changes in its rotation, which is crucial in determining the natural frequency of free transverse vibrations in a shaft, and is influenced by the shaft's length, load per unit length, and modulus of elasticity. Moment of inertia of shaft is denoted by I_shaft symbol.

How to evaluate Moment of Inertia of Shaft given Static Deflection given Load per Unit Length using this online evaluator? To use this online evaluator for Moment of Inertia of Shaft given Static Deflection given Load per Unit Length, enter Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Static Deflection (δ) and hit the calculate button.

FAQs on Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

What is the formula to find Moment of Inertia of Shaft given Static Deflection given Load per Unit Length?

The formula of Moment of Inertia of Shaft given Static Deflection given Load per Unit Length is expressed as Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection). Here is an example- 5.427608 = (5*3*3.5^4)/(384*15*0.072).

How to calculate Moment of Inertia of Shaft given Static Deflection given Load per Unit Length?

With Load per unit length (w), Length of Shaft (L_shaft), Young's Modulus (E) & Static Deflection (δ) we can find Moment of Inertia of Shaft given Static Deflection given Load per Unit Length using the formula - Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection).

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=(4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity)
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)

Can the Moment of Inertia of Shaft given Static Deflection given Load per Unit Length be negative?

No, the Moment of Inertia of Shaft given Static Deflection given Load per Unit Length, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Moment of Inertia of Shaft given Static Deflection given Load per Unit Length?

Moment of Inertia of Shaft given Static Deflection given Load per Unit Length 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 Static Deflection given Load per Unit Length can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

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

​GoMoment of Inertia of Shaft given Natural Frequency Formula

​GoMoment of Inertia of Shaft given Circular Frequency Formula

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

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

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

FAQs on Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

Variable Name

GoMoment of Inertia of Shaft given Natural Frequency Formula

GoMoment of Inertia of Shaft given Circular Frequency Formula