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Moment of Inertia of Shaft given Static Deflection 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{W attached \cdot {L shaft}^{3}}{3 \cdot E \cdot δ}

I_shaft - Moment of inertia of shaft?W_attached - Load Attached to Free End of Constraint?L_shaft - Length of Shaft?E - Young's Modulus?δ - Static Deflection?

Moment of Inertia of Shaft given Static Deflection Example

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

Here is how the Moment of Inertia of Shaft given Static Deflection equation looks like.

6 = \frac{0.4534 \cdot {3.5}^{3}}{3 \cdot 15 \cdot 0.072}

6kg·m² = \frac{0.4534kg \cdot {3.5m}^{3}}{3 \cdot 15N/m \cdot 0.072m}

6 = \frac{0.4534 \cdot {3.5}^{3}}{3 \cdot 15 \cdot 0.072}

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Moment of Inertia of Shaft given Static Deflection Solution

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

FIRST Step Consider the formula

I shaft = \frac{W attached \cdot {L shaft}^{3}}{3 \cdot E \cdot δ}

Next Step Substitute values of Variables

∴

I shaft = \frac{0.4534kg \cdot {3.5m}^{3}}{3 \cdot 15N/m \cdot 0.072m}

Next Step Prepare to Evaluate

∴

I shaft = \frac{0.4534 \cdot {3.5}^{3}}{3 \cdot 15 \cdot 0.072}

Next Step Evaluate

∴

I shaft = 5.99999895833333kg·m²

LAST Step Rounding Answer

∴

I shaft = 6kg·m²

Moment of Inertia of Shaft given Static Deflection 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 Attached to Free End of Constraint

Load Attached to Free End of Constraint is the force applied to the free end of a constraint in a system undergoing free transverse vibrations.

Symbol: W_attached

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Load Attached to Free End of Constraint

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 in General Shaft category

Go Static Deflection given Moment of Inertia of Shaft

δ = \frac{W attached \cdot {L shaft}^{3}}{3 \cdot E \cdot I shaft}

Go Load at Free End in Free Transverse Vibrations

W attached = \frac{δ \cdot 3 \cdot E \cdot I shaft}{{L shaft}^{3}}

Go Length of Shaft

L shaft = {(\frac{δ \cdot 3 \cdot E \cdot I shaft}{W attached})}^{\frac{1}{3}}

Go Natural Frequency of Free Transverse Vibrations

f = \frac{\sqrt{\frac{s}{W attached}}}{2} \cdot π

How to Evaluate Moment of Inertia of Shaft given Static Deflection?

Moment of Inertia of Shaft given Static Deflection evaluator uses Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection) to evaluate the Moment of inertia of shaft, Moment of Inertia of Shaft given Static Deflection formula is defined as a measure of the shaft's resistance to changes in its rotation, which is essential in determining the natural frequency of free transverse vibrations, and is influenced by the attached weight, length, and static deflection of the shaft. Moment of inertia of shaft is denoted by I_shaft symbol.

How to evaluate Moment of Inertia of Shaft given Static Deflection using this online evaluator? To use this online evaluator for Moment of Inertia of Shaft given Static Deflection, enter Load Attached to Free End of Constraint (W_attached), 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

What is the formula to find Moment of Inertia of Shaft given Static Deflection?

The formula of Moment of Inertia of Shaft given Static Deflection is expressed as Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection). Here is an example- 5.999999 = (0.453411*3.5^3)/(3*15*0.072).

How to calculate Moment of Inertia of Shaft given Static Deflection?

With Load Attached to Free End of Constraint (W_attached), Length of Shaft (L_shaft), Young's Modulus (E) & Static Deflection (δ) we can find Moment of Inertia of Shaft given Static Deflection using the formula - Moment of inertia of shaft = (Load Attached to Free End of Constraint*Length of Shaft^3)/(3*Young's Modulus*Static Deflection).

Can the Moment of Inertia of Shaft given Static Deflection be negative?

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

Which unit is used to measure Moment of Inertia of Shaft given Static Deflection?

Moment of Inertia of Shaft given Static Deflection 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 can be measured.

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Moment of Inertia of Shaft given Static Deflection Formula

Moment of Inertia of Shaft given Static Deflection Example

Moment of Inertia of Shaft given Static Deflection Solution

Moment of Inertia of Shaft given Static Deflection Formula Elements

Other formulas in General Shaft category

How to Evaluate Moment of Inertia of Shaft given Static Deflection?

FAQs on Moment of Inertia of Shaft given Static Deflection

Variable Name