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Final Angular Velocity of Body given Kinetic Energy of Rotating Body Formula

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Final Angular Velocity of Braked System is the velocity at which the system or the object is rotating after the brakes are totally applied. Check FAQs

ω 2 = \sqrt{{ω 1}^{2} - (2 \cdot \frac{KE}{I})}

ω₂ - Final Angular Velocity of Braked System?ω₁ - Initial Angular Velocity of Braked System?KE - Kinetic Energy Absorbed by Brake?I - Moment of Inertia of Braked Assembly?

Final Angular Velocity of Body given Kinetic Energy of Rotating Body Example

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Here is how the Final Angular Velocity of Body given Kinetic Energy of Rotating Body equation looks like with Values.

Here is how the Final Angular Velocity of Body given Kinetic Energy of Rotating Body equation looks like with Units.

Here is how the Final Angular Velocity of Body given Kinetic Energy of Rotating Body equation looks like.

0.4732 = \sqrt{{36.65}^{2} - (2 \cdot \frac{94950}{141.4})}

0.4732rad/s = \sqrt{{36.65rad/s}^{2} - (2 \cdot \frac{94950J}{141.4kg·m²})}

0.4732 = \sqrt{{36.65}^{2} - (2 \cdot \frac{94950}{141.4})}

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Final Angular Velocity of Body given Kinetic Energy of Rotating Body Solution

Follow our step by step solution on how to calculate Final Angular Velocity of Body given Kinetic Energy of Rotating Body?

FIRST Step Consider the formula

ω 2 = \sqrt{{ω 1}^{2} - (2 \cdot \frac{KE}{I})}

Next Step Substitute values of Variables

∴

ω 2 = \sqrt{{36.65rad/s}^{2} - (2 \cdot \frac{94950J}{141.4kg·m²})}

Next Step Prepare to Evaluate

∴

ω 2 = \sqrt{{36.65}^{2} - (2 \cdot \frac{94950}{141.4})}

Next Step Evaluate

∴

ω 2 = 0.473195971196757rad/s

LAST Step Rounding Answer

∴

ω 2 = 0.4732rad/s

Final Angular Velocity of Body given Kinetic Energy of Rotating Body Formula Elements

Variables

Functions

Final Angular Velocity of Braked System

Final Angular Velocity of Braked System is the velocity at which the system or the object is rotating after the brakes are totally applied.

Symbol: ω₂

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Final Angular Velocity of Braked System

Initial Angular Velocity of Braked System

Initial Angular Velocity of Braked System is the velocity at which the system or the object is rotating before the brakes are applied.

Symbol: ω₁

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Initial Angular Velocity of Braked System

Kinetic Energy Absorbed by Brake

Kinetic Energy Absorbed by Brake is defined as the energy absorbed by the braking system.

Symbol: KE

Measurement: EnergyUnit: J

Note: Value should be greater than 0.

Formulas to find Kinetic Energy Absorbed by Brake

Moment of Inertia of Braked Assembly

Moment of Inertia of Braked Assembly is the measure of the resistance of a body to angular acceleration about a given axis.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia of Braked Assembly

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 Energy and Thermal Equation category

Go Kinetic Energy Absorbed by Brake

KE = m \cdot \frac{u^{2} - v^{2}}{2}

Go Mass of System given Kinetic Energy Absorbed by Brakes

m = 2 \cdot \frac{KE}{u^{2} - v^{2}}

Go Initial Velocity of System given Kinetic Energy Absorbed by Brakes

u = \sqrt{(2 \cdot \frac{KE}{m}) + v^{2}}

Go Final Velocity given Kinetic Energy Absorbed by Brakes

v = \sqrt{u^{2} - (2 \cdot \frac{KE}{m})}

How to Evaluate Final Angular Velocity of Body given Kinetic Energy of Rotating Body?

Final Angular Velocity of Body given Kinetic Energy of Rotating Body evaluator uses Final Angular Velocity of Braked System = sqrt(Initial Angular Velocity of Braked System^2-(2*Kinetic Energy Absorbed by Brake/Moment of Inertia of Braked Assembly)) to evaluate the Final Angular Velocity of Braked System, Final Angular Velocity of Body given Kinetic Energy of Rotating Body is the speed of rotation at which the energy associated with the body's motion equals the kinetic energy, calculated using the moment of inertia. Final Angular Velocity of Braked System is denoted by ω₂ symbol.

How to evaluate Final Angular Velocity of Body given Kinetic Energy of Rotating Body using this online evaluator? To use this online evaluator for Final Angular Velocity of Body given Kinetic Energy of Rotating Body, enter Initial Angular Velocity of Braked System (ω₁), Kinetic Energy Absorbed by Brake (KE) & Moment of Inertia of Braked Assembly (I) and hit the calculate button.

FAQs on Final Angular Velocity of Body given Kinetic Energy of Rotating Body

What is the formula to find Final Angular Velocity of Body given Kinetic Energy of Rotating Body?

The formula of Final Angular Velocity of Body given Kinetic Energy of Rotating Body is expressed as Final Angular Velocity of Braked System = sqrt(Initial Angular Velocity of Braked System^2-(2*Kinetic Energy Absorbed by Brake/Moment of Inertia of Braked Assembly)). Here is an example- 0.473196 = sqrt(36.65^2-(2*94950/141.4)).

How to calculate Final Angular Velocity of Body given Kinetic Energy of Rotating Body?

With Initial Angular Velocity of Braked System (ω₁), Kinetic Energy Absorbed by Brake (KE) & Moment of Inertia of Braked Assembly (I) we can find Final Angular Velocity of Body given Kinetic Energy of Rotating Body using the formula - Final Angular Velocity of Braked System = sqrt(Initial Angular Velocity of Braked System^2-(2*Kinetic Energy Absorbed by Brake/Moment of Inertia of Braked Assembly)). This formula also uses Square Root (sqrt) function(s).

Can the Final Angular Velocity of Body given Kinetic Energy of Rotating Body be negative?

No, the Final Angular Velocity of Body given Kinetic Energy of Rotating Body, measured in Angular Velocity cannot be negative.

Which unit is used to measure Final Angular Velocity of Body given Kinetic Energy of Rotating Body?

Final Angular Velocity of Body given Kinetic Energy of Rotating Body 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 Final Angular Velocity of Body given Kinetic Energy of Rotating Body can be measured.

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Final Angular Velocity of Body given Kinetic Energy of Rotating Body Formula

Final Angular Velocity of Body given Kinetic Energy of Rotating Body Example

Final Angular Velocity of Body given Kinetic Energy of Rotating Body Solution

Final Angular Velocity of Body given Kinetic Energy of Rotating Body Formula Elements

Other formulas in Energy and Thermal Equation category

How to Evaluate Final Angular Velocity of Body given Kinetic Energy of Rotating Body?

FAQs on Final Angular Velocity of Body given Kinetic Energy of Rotating Body

Variable Name