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Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint Formula

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Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system. Check FAQs

I c = \frac{6 \cdot KE}{{ω f}^{2}}

I_c - Total Mass Moment of Inertia?KE - Kinetic Energy?ω_f - Angular Velocity of Free End?

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint Example

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Here is how the Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint equation looks like.

10.65 = \frac{6 \cdot 900}{{22.5176}^{2}}

10.65kg·m² = \frac{6 \cdot 900J}{{22.5176rad/s}^{2}}

10.65 = \frac{6 \cdot 900}{{22.5176}^{2}}

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Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint Solution

Follow our step by step solution on how to calculate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?

FIRST Step Consider the formula

I c = \frac{6 \cdot KE}{{ω f}^{2}}

Next Step Substitute values of Variables

∴

I c = \frac{6 \cdot 900J}{{22.5176rad/s}^{2}}

Next Step Prepare to Evaluate

∴

I c = \frac{6 \cdot 900}{{22.5176}^{2}}

Next Step Evaluate

∴

I c = 10.6499988187495kg·m²

LAST Step Rounding Answer

∴

I c = 10.65kg·m²

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint Formula Elements

Variables

Total Mass Moment of Inertia

Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system.

Symbol: I_c

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Total Mass Moment of Inertia

Kinetic Energy

Kinetic Energy is the energy of an object due to its motion, particularly in the context of torsional vibrations, where it is related to the twisting motion.

Symbol: KE

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Kinetic Energy

Angular Velocity of Free End

Angular Velocity of Free End is the rotational speed of the free end of a torsional vibration system, measuring its oscillatory motion around a fixed axis.

Symbol: ω_f

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity of Free End

Other formulas in Effect of Inertia of Constraint on Torsional Vibrations category

Go Mass Moment of Inertia of Element

I = \frac{δ x \cdot I c}{l}

Go Angular Velocity of Element

ω = \frac{ω f \cdot x}{l}

Go Kinetic Energy Possessed by Element

KE = \frac{I c \cdot {(ω f \cdot x)}^{2} \cdot δ x}{2 \cdot l^{3}}

Go Total Kinetic Energy of Constraint

KE = \frac{I c \cdot {ω f}^{2}}{6}

How to Evaluate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint evaluator uses Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2) to evaluate the Total Mass Moment of Inertia, Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint formula is defined as a measure of the rotational inertia of an object undergoing torsional vibrations, which is a critical parameter in understanding the vibrational behavior of mechanical systems. Total Mass Moment of Inertia is denoted by I_c symbol.

How to evaluate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint using this online evaluator? To use this online evaluator for Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint, enter Kinetic Energy (KE) & Angular Velocity of Free End (ω_f) and hit the calculate button.

FAQs on Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint

What is the formula to find Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?

The formula of Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint is expressed as Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2). Here is an example- 10.65 = (6*900)/(22.5176^2).

How to calculate Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?

With Kinetic Energy (KE) & Angular Velocity of Free End (ω_f) we can find Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint using the formula - Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2).

Can the Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint be negative?

No, the Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint, measured in Moment of Inertia cannot be negative.

Which unit is used to measure Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint?

Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint 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 Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint can be measured.

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