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Moment of Inertia of Disc using Natural Frequency of Vibration Formula

GoMoment of Inertia of Disc given Time Period of Vibration Formula

GoMoment of Inertia of Disc given Angular Velocity Formula

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Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis. Check FAQs

I d = \frac{q}{{(2 \cdot π \cdot f n)}^{2}}

I_d - Mass Moment of Inertia of Disc?q - Torsional Stiffness?f_n - Natural Frequency?π - Archimedes' constant?

Moment of Inertia of Disc using Natural Frequency of Vibration Example

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Here is how the Moment of Inertia of Disc using Natural Frequency of Vibration equation looks like with Values.

Here is how the Moment of Inertia of Disc using Natural Frequency of Vibration equation looks like with Units.

Here is how the Moment of Inertia of Disc using Natural Frequency of Vibration equation looks like.

6.2 = \frac{5.4}{{(2 \cdot 3.1416 \cdot 0.1485)}^{2}}

6.2kg·m² = \frac{5.4N/m}{{(2 \cdot 3.1416 \cdot 0.1485Hz)}^{2}}

6.2 = \frac{5.4}{{(2 \cdot 3.1416 \cdot 0.1485)}^{2}}

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Moment of Inertia of Disc using Natural Frequency of Vibration Solution

Follow our step by step solution on how to calculate Moment of Inertia of Disc using Natural Frequency of Vibration?

FIRST Step Consider the formula

I d = \frac{q}{{(2 \cdot π \cdot f n)}^{2}}

Next Step Substitute values of Variables

∴

I d = \frac{5.4N/m}{{(2 \cdot π \cdot 0.1485Hz)}^{2}}

Next Step Substitute values of Constants

∴

I d = \frac{5.4N/m}{{(2 \cdot 3.1416 \cdot 0.1485Hz)}^{2}}

Next Step Prepare to Evaluate

∴

I d = \frac{5.4}{{(2 \cdot 3.1416 \cdot 0.1485)}^{2}}

Next Step Evaluate

∴

I d = 6.20003248918117kg·m²

LAST Step Rounding Answer

∴

I d = 6.2kg·m²

Moment of Inertia of Disc using Natural Frequency of Vibration Formula Elements

Variables

Constants

Mass Moment of Inertia of Disc

Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.

Symbol: I_d

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Mass Moment of Inertia of Disc

Torsional Stiffness

torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.

Symbol: q

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Torsional Stiffness

Natural Frequency

Natural Frequency is the number of oscillations or cycles per second in a torsional vibration system, characterizing its inherent oscillatory behavior.

Symbol: f_n

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Natural Frequency

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 Mass Moment of Inertia of Disc

Go Moment of Inertia of Disc given Time Period of Vibration

I d = \frac{{t p}^{2} \cdot q}{{(2 \cdot π)}^{2}}

Go Moment of Inertia of Disc given Angular Velocity

I d = \frac{q r}{ω^{2}}

Other formulas in Natural Frequency of Free Torsional Vibrations category

Go Torsional Stiffness of Shaft given Natural Frequency of Vibration

q = {(2 \cdot π \cdot f n)}^{2} \cdot I d

Go Torsional Stiffness of Shaft given Time Period of Vibration

q = \frac{{(2 \cdot π)}^{2} \cdot I d}{{(t p)}^{2}}

Go Time Period for Vibrations

t p = 2 \cdot π \cdot \sqrt{\frac{I d}{q}}

Go Torsional Stiffness of Shaft given Angular Velocity

q r = ω^{2} \cdot I d

How to Evaluate Moment of Inertia of Disc using Natural Frequency of Vibration?

Moment of Inertia of Disc using Natural Frequency of Vibration evaluator uses Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2) to evaluate the Mass Moment of Inertia of Disc, Moment of Inertia of Disc using Natural Frequency of Vibration formula is defined as a measure of an object's resistance to changes in its rotation, calculated using the natural frequency of vibration, providing valuable insights into the disc's rotational motion and stability in torsional vibrations. Mass Moment of Inertia of Disc is denoted by I_d symbol.

How to evaluate Moment of Inertia of Disc using Natural Frequency of Vibration using this online evaluator? To use this online evaluator for Moment of Inertia of Disc using Natural Frequency of Vibration, enter Torsional Stiffness (q) & Natural Frequency (f_n) and hit the calculate button.

FAQs on Moment of Inertia of Disc using Natural Frequency of Vibration

What is the formula to find Moment of Inertia of Disc using Natural Frequency of Vibration?

The formula of Moment of Inertia of Disc using Natural Frequency of Vibration is expressed as Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2). Here is an example- 6.200032 = 5.4/((2*pi*0.148532)^2).

How to calculate Moment of Inertia of Disc using Natural Frequency of Vibration?

With Torsional Stiffness (q) & Natural Frequency (f_n) we can find Moment of Inertia of Disc using Natural Frequency of Vibration using the formula - Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Natural Frequency)^2). This formula also uses Archimedes' constant .

What are the other ways to Calculate Mass Moment of Inertia of Disc?

Here are the different ways to Calculate Mass Moment of Inertia of Disc-

Mass Moment of Inertia of Disc=(Time Period^2*Torsional Stiffness)/((2*pi)^2)
Mass Moment of Inertia of Disc=Resistance Torsional Stiffness/(Angular Velocity^2)

Can the Moment of Inertia of Disc using Natural Frequency of Vibration be negative?

No, the Moment of Inertia of Disc using Natural Frequency of Vibration, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Moment of Inertia of Disc using Natural Frequency of Vibration?

Moment of Inertia of Disc using Natural Frequency of Vibration 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 Disc using Natural Frequency of Vibration can be measured.

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Moment of Inertia of Disc using Natural Frequency of Vibration Formula

​GoMoment of Inertia of Disc given Time Period of Vibration Formula

​GoMoment of Inertia of Disc given Angular Velocity Formula

Moment of Inertia of Disc using Natural Frequency of Vibration Example

Moment of Inertia of Disc using Natural Frequency of Vibration Solution

Moment of Inertia of Disc using Natural Frequency of Vibration Formula Elements

Other Formulas to find Mass Moment of Inertia of Disc

Other formulas in Natural Frequency of Free Torsional Vibrations category

How to Evaluate Moment of Inertia of Disc using Natural Frequency of Vibration?

FAQs on Moment of Inertia of Disc using Natural Frequency of Vibration

Variable Name

GoMoment of Inertia of Disc given Time Period of Vibration Formula

GoMoment of Inertia of Disc given Angular Velocity Formula