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Moment of Inertia of Disc given Angular Velocity Formula

GoMoment of Inertia of Disc using Natural Frequency of Vibration Formula

GoMoment of Inertia of Disc given Time Period of Vibration 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 r}{ω^{2}}

I_d - Mass Moment of Inertia of Disc?q_r - Resistance Torsional Stiffness?ω - Angular Velocity?

Moment of Inertia of Disc given Angular Velocity Example

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Here is how the Moment of Inertia of Disc given Angular Velocity equation looks like with Values.

Here is how the Moment of Inertia of Disc given Angular Velocity equation looks like with Units.

Here is how the Moment of Inertia of Disc given Angular Velocity equation looks like.

6.2 = \frac{777.728}{{11.2}^{2}}

6.2kg·m² = \frac{777.728N/m}{{11.2rad/s}^{2}}

6.2 = \frac{777.728}{{11.2}^{2}}

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Moment of Inertia of Disc given Angular Velocity Solution

Follow our step by step solution on how to calculate Moment of Inertia of Disc given Angular Velocity?

FIRST Step Consider the formula

I d = \frac{q r}{ω^{2}}

Next Step Substitute values of Variables

∴

I d = \frac{777.728N/m}{{11.2rad/s}^{2}}

Next Step Prepare to Evaluate

∴

I d = \frac{777.728}{{11.2}^{2}}

LAST Step Evaluate

∴

I d = 6.2kg·m²

Moment of Inertia of Disc given Angular Velocity Formula Elements

Variables

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

Resistance Torsional Stiffness

Resistance Torsional Stiffness is the resistance of an object to twisting or rotational deformation, measured by the amount of torque required to produce a unit of angular deformation.

Symbol: q_r

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Resistance Torsional Stiffness

Angular Velocity

Angular Velocity is the measure of how quickly an object rotates or revolves around a central axis in a torsional vibration system.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

Other Formulas to find Mass Moment of Inertia of Disc

Go Moment of Inertia of Disc using Natural Frequency of Vibration

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

Go Moment of Inertia of Disc given Time Period of Vibration

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

Moment of Inertia of Disc given Angular Velocity evaluator uses Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2) to evaluate the Mass Moment of Inertia of Disc, Moment of Inertia of Disc given Angular Velocity formula is defined as a measure of an object's resistance to changes in its rotation, which is essential in understanding the behavior of rotating systems, particularly in the context of torsional vibrations. Mass Moment of Inertia of Disc is denoted by I_d symbol.

How to evaluate Moment of Inertia of Disc given Angular Velocity using this online evaluator? To use this online evaluator for Moment of Inertia of Disc given Angular Velocity, enter Resistance Torsional Stiffness (q_r) & Angular Velocity (ω) and hit the calculate button.

FAQs on Moment of Inertia of Disc given Angular Velocity

What is the formula to find Moment of Inertia of Disc given Angular Velocity?

The formula of Moment of Inertia of Disc given Angular Velocity is expressed as Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2). Here is an example- 6.2 = 777.728/(11.2^2).

How to calculate Moment of Inertia of Disc given Angular Velocity?

With Resistance Torsional Stiffness (q_r) & Angular Velocity (ω) we can find Moment of Inertia of Disc given Angular Velocity using the formula - Mass Moment of Inertia of Disc = Resistance Torsional Stiffness/(Angular Velocity^2).

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=Torsional Stiffness/((2*pi*Natural Frequency)^2)
Mass Moment of Inertia of Disc=(Time Period^2*Torsional Stiffness)/((2*pi)^2)

Can the Moment of Inertia of Disc given Angular Velocity be negative?

No, the Moment of Inertia of Disc given Angular Velocity, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Moment of Inertia of Disc given Angular Velocity?

Moment of Inertia of Disc given Angular Velocity 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 given Angular Velocity can be measured.

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Moment of Inertia of Disc given Angular Velocity Formula

​GoMoment of Inertia of Disc using Natural Frequency of Vibration Formula

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

Moment of Inertia of Disc given Angular Velocity Example

Moment of Inertia of Disc given Angular Velocity Solution

Moment of Inertia of Disc given Angular Velocity 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 given Angular Velocity?

FAQs on Moment of Inertia of Disc given Angular Velocity

Variable Name

GoMoment of Inertia of Disc using Natural Frequency of Vibration Formula

GoMoment of Inertia of Disc given Time Period of Vibration Formula