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Angular Velocity of Free End using Kinetic Energy of Constraint Formula

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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. Check FAQs

ω f = \sqrt{\frac{6 \cdot KE}{I c}}

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

Angular Velocity of Free End using Kinetic Energy of Constraint Example

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Here is how the Angular Velocity of Free End using Kinetic Energy of Constraint equation looks like with Values.

Here is how the Angular Velocity of Free End using Kinetic Energy of Constraint equation looks like with Units.

Here is how the Angular Velocity of Free End using Kinetic Energy of Constraint equation looks like.

22.5176 = \sqrt{\frac{6 \cdot 900}{10.65}}

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

22.5176 = \sqrt{\frac{6 \cdot 900}{10.65}}

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Angular Velocity of Free End using Kinetic Energy of Constraint Solution

Follow our step by step solution on how to calculate Angular Velocity of Free End using Kinetic Energy of Constraint?

FIRST Step Consider the formula

ω f = \sqrt{\frac{6 \cdot KE}{I c}}

Next Step Substitute values of Variables

∴

ω f = \sqrt{\frac{6 \cdot 900J}{10.65kg·m²}}

Next Step Prepare to Evaluate

∴

ω f = \sqrt{\frac{6 \cdot 900}{10.65}}

Next Step Evaluate

∴

ω f = 22.517598751224rad/s

LAST Step Rounding Answer

∴

ω f = 22.5176rad/s

Angular Velocity of Free End using Kinetic Energy of Constraint Formula Elements

Variables

Functions

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 Angular Velocity of Free End using Kinetic Energy of Constraint?

Angular Velocity of Free End using Kinetic Energy of Constraint evaluator uses Angular Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass Moment of Inertia) to evaluate the Angular Velocity of Free End, Angular Velocity of Free End using Kinetic Energy of Constraint formula is defined as a measure of the rotational speed of a free end in a torsional vibration system, which is influenced by the kinetic energy of the constraint and the moment of inertia of the system. Angular Velocity of Free End is denoted by ω_f symbol.

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

FAQs on Angular Velocity of Free End using Kinetic Energy of Constraint

What is the formula to find Angular Velocity of Free End using Kinetic Energy of Constraint?

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

How to calculate Angular Velocity of Free End using Kinetic Energy of Constraint?

With Kinetic Energy (KE) & Total Mass Moment of Inertia (I_c) we can find Angular Velocity of Free End using Kinetic Energy of Constraint using the formula - Angular Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass Moment of Inertia). This formula also uses Square Root (sqrt) function(s).

Can the Angular Velocity of Free End using Kinetic Energy of Constraint be negative?

No, the Angular Velocity of Free End using Kinetic Energy of Constraint, measured in Angular Velocity cannot be negative.

Which unit is used to measure Angular Velocity of Free End using Kinetic Energy of Constraint?

Angular Velocity of Free End using Kinetic Energy of Constraint is usually measured using the Radian per Second[rad/s] for Angular Velocity. Radian per Day[rad/s], Radian per Hour[rad/s], Radian per Minute[rad/s] are the few other units in which Angular Velocity of Free End using Kinetic Energy of Constraint can be measured.

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