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Kinetic Energy Possessed by Element Formula

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GoTotal Kinetic Energy of Constraint 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 \cdot x)}^{2} \cdot δ x}{2 \cdot l^{3}}

KE - Kinetic Energy?I_c - Total Mass Moment of Inertia?ω_f - Angular Velocity of Free End?x - Distance Between Small Element and Fixed End?δ_x - Length of Small Element?l - Length of Constraint?

Kinetic Energy Possessed by Element Example

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Here is how the Kinetic Energy Possessed by Element equation looks like with Values.

Here is how the Kinetic Energy Possessed by Element equation looks like with Units.

Here is how the Kinetic Energy Possessed by Element equation looks like.

901.8318 = \frac{10.65 \cdot {(22.5176 \cdot 3.66)}^{2} \cdot 9.82}{2 \cdot {7.33}^{3}}

901.8318J = \frac{10.65kg·m² \cdot {(22.5176rad/s \cdot 3.66mm)}^{2} \cdot 9.82mm}{2 \cdot {7.33mm}^{3}}

901.8318 = \frac{10.65 \cdot {(22.5176 \cdot 3.66)}^{2} \cdot 9.82}{2 \cdot {7.33}^{3}}

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Kinetic Energy Possessed by Element Solution

Follow our step by step solution on how to calculate Kinetic Energy Possessed by Element?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

KE = \frac{10.65kg·m² \cdot {(22.5176rad/s \cdot 3.66mm)}^{2} \cdot 9.82mm}{2 \cdot {7.33mm}^{3}}

Next Step Convert Units

∴

KE = \frac{10.65kg·m² \cdot {(22.5176rad/s \cdot 0.0037m)}^{2} \cdot 0.0098m}{2 \cdot {0.0073m}^{3}}

Next Step Prepare to Evaluate

∴

KE = \frac{10.65 \cdot {(22.5176 \cdot 0.0037)}^{2} \cdot 0.0098}{2 \cdot {0.0073}^{3}}

Next Step Evaluate

∴

KE = 901.83180381676J

LAST Step Rounding Answer

∴

KE = 901.8318J

Kinetic Energy Possessed by Element 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

Open Variable

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

Open Variable

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

Open Variable

Distance Between Small Element and Fixed End

Distance Between Small Element and Fixed End is the length between a small element in a shaft and its fixed end in a torsional vibration system.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance Between Small Element and Fixed End

Open Variable

Length of Small Element

Length of Small Element is the distance of a small portion of a shaft in torsional vibrations, used to calculate the angular displacement of the shaft.

Symbol: δ_x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Small Element

Open Variable

Length of Constraint

Length of Constraint is the distance between the point of application of the torsional load and the axis of rotation of the shaft.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Constraint

Open Variable

Other Formulas to find Kinetic Energy

Go Total Kinetic Energy of Constraint

KE = \frac{I c \cdot {ω f}^{2}}{6}

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}}

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How to Evaluate Kinetic Energy Possessed by Element?

Kinetic Energy Possessed by Element evaluator uses 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) to evaluate the Kinetic Energy, Kinetic Energy Possessed by Element formula is defined as the energy associated with an object's motion in a torsional vibration system, which is a critical concept in mechanical engineering and physics, particularly in the study of rotational motion and oscillations. Kinetic Energy is denoted by KE symbol.

How to evaluate Kinetic Energy Possessed by Element using this online evaluator? To use this online evaluator for Kinetic Energy Possessed by Element, enter Total Mass Moment of Inertia (I_c), Angular Velocity of Free End (ω_f), Distance Between Small Element and Fixed End (x), Length of Small Element (δ_x) & Length of Constraint (l) and hit the calculate button.

FAQs on Kinetic Energy Possessed by Element

What is the formula to find Kinetic Energy Possessed by Element?

The formula of Kinetic Energy Possessed by Element is expressed as 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). Here is an example- 901.8318 = (10.65*(22.5176*0.00366)^2*0.00982)/(2*0.00733^3).

How to calculate Kinetic Energy Possessed by Element?

With Total Mass Moment of Inertia (I_c), Angular Velocity of Free End (ω_f), Distance Between Small Element and Fixed End (x), Length of Small Element (δ_x) & Length of Constraint (l) we can find Kinetic Energy Possessed by Element using the formula - 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).

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^2)/6

Can the Kinetic Energy Possessed by Element be negative?

Yes, the Kinetic Energy Possessed by Element, measured in Energy can be negative.

Which unit is used to measure Kinetic Energy Possessed by Element?

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

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