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Total Kinetic Energy of Constraint Formula

GoKinetic Energy Possessed by Element Formula

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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. Check FAQs

KE = \frac{I c \cdot {ω f}^{2}}{6}

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

Total Kinetic Energy of Constraint Example

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Here is how the Total Kinetic Energy of Constraint equation looks like with Values.

Here is how the Total Kinetic Energy of Constraint equation looks like with Units.

Here is how the Total Kinetic Energy of Constraint equation looks like.

900.0001 = \frac{10.65 \cdot {22.5176}^{2}}{6}

900.0001J = \frac{10.65kg·m² \cdot {22.5176rad/s}^{2}}{6}

900.0001 = \frac{10.65 \cdot {22.5176}^{2}}{6}

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Total Kinetic Energy of Constraint Solution

Follow our step by step solution on how to calculate Total Kinetic Energy of Constraint?

FIRST Step Consider the formula

KE = \frac{I c \cdot {ω f}^{2}}{6}

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

KE = 900.000099824J

LAST Step Rounding Answer

∴

KE = 900.0001J

Total Kinetic Energy of Constraint Formula Elements

Variables

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

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

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 to find Kinetic Energy

Go Kinetic Energy Possessed by Element

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

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

I c = \frac{6 \cdot KE}{{ω f}^{2}}

Go Angular Velocity of Free End using Kinetic Energy of Constraint

ω f = \sqrt{\frac{6 \cdot KE}{I c}}

How to Evaluate Total Kinetic Energy of Constraint?

Total Kinetic Energy of Constraint evaluator uses Kinetic Energy = (Total Mass Moment of Inertia*Angular Velocity of Free End^2)/6 to evaluate the Kinetic Energy, Total Kinetic Energy of Constraint formula is defined as the energy associated with the rotational motion of a system in torsional vibrations, where the system's inertia and angular frequency are key factors in determining this energy. Kinetic Energy is denoted by KE symbol.

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

FAQs on Total Kinetic Energy of Constraint

What is the formula to find Total Kinetic Energy of Constraint?

The formula of Total Kinetic Energy of Constraint is expressed as Kinetic Energy = (Total Mass Moment of Inertia*Angular Velocity of Free End^2)/6. Here is an example- 900.0001 = (10.65*22.5176^2)/6.

How to calculate Total Kinetic Energy of Constraint?

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

What are the other ways to Calculate Kinetic Energy?

Here are the different ways to Calculate Kinetic Energy-

Kinetic Energy=(Total Mass Moment of Inertia*(Angular Velocity of Free End*Distance Between Small Element and Fixed End)^2*Length of Small Element)/(2*Length of Constraint^3)

Can the Total Kinetic Energy of Constraint be negative?

Yes, the Total Kinetic Energy of Constraint, measured in Energy can be negative.

Which unit is used to measure Total Kinetic Energy of Constraint?

Total Kinetic Energy of Constraint is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Total Kinetic Energy of Constraint can be measured.

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