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Radius of Gyration given Kinetic Energy of Rotating Body Formula

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Radius of Gyration of Braked System is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass. Check FAQs

k g = \sqrt{2 \cdot \frac{KE}{m \cdot ({ω 1}^{2} - {ω 2}^{2})}}

k_g - Radius of Gyration of Braked System?KE - Kinetic Energy Absorbed by Brake?m - Mass of Brake Assembly?ω₁ - Initial Angular Velocity of Braked System?ω₂ - Final Angular Velocity of Braked System?

Radius of Gyration given Kinetic Energy of Rotating Body Example

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Here is how the Radius of Gyration given Kinetic Energy of Rotating Body equation looks like with Values.

Here is how the Radius of Gyration given Kinetic Energy of Rotating Body equation looks like with Units.

Here is how the Radius of Gyration given Kinetic Energy of Rotating Body equation looks like.

353.7472 = \sqrt{2 \cdot \frac{94950}{1130 \cdot ({36.65}^{2} - {0.52}^{2})}}

353.7472mm = \sqrt{2 \cdot \frac{94950J}{1130kg \cdot ({36.65rad/s}^{2} - {0.52rad/s}^{2})}}

353.7472 = \sqrt{2 \cdot \frac{94950}{1130 \cdot ({36.65}^{2} - {0.52}^{2})}}

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Radius of Gyration given Kinetic Energy of Rotating Body Solution

Follow our step by step solution on how to calculate Radius of Gyration given Kinetic Energy of Rotating Body?

FIRST Step Consider the formula

k g = \sqrt{2 \cdot \frac{KE}{m \cdot ({ω 1}^{2} - {ω 2}^{2})}}

Next Step Substitute values of Variables

∴

k g = \sqrt{2 \cdot \frac{94950J}{1130kg \cdot ({36.65rad/s}^{2} - {0.52rad/s}^{2})}}

Next Step Prepare to Evaluate

∴

k g = \sqrt{2 \cdot \frac{94950}{1130 \cdot ({36.65}^{2} - {0.52}^{2})}}

Next Step Evaluate

∴

k g = 0.353747190471113m

Next Step Convert to Output's Unit

∴

k g = 353.747190471113mm

LAST Step Rounding Answer

∴

k g = 353.7472mm

Radius of Gyration given Kinetic Energy of Rotating Body Formula Elements

Variables

Functions

Radius of Gyration of Braked System

Radius of Gyration of Braked System is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.

Symbol: k_g

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration 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

Mass of Brake Assembly

Mass of Brake Assembly is defined as the summation of mass of all the objects present in the system on which brakes are applied.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Brake Assembly

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

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

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 Radius of Gyration given Kinetic Energy of Rotating Body?

Radius of Gyration given Kinetic Energy of Rotating Body evaluator uses Radius of Gyration of Braked System = sqrt(2*Kinetic Energy Absorbed by Brake/(Mass of Brake Assembly*(Initial Angular Velocity of Braked System^2-Final Angular Velocity of Braked System^2))) to evaluate the Radius of Gyration of Braked System, The Radius of Gyration given Kinetic Energy of Rotating Body formula is defined as radial distance to point which would have moment of inertia same as body's actual distribution of mass, if total mass of body were concentrated there. Radius of Gyration of Braked System is denoted by k_g symbol.

How to evaluate Radius of Gyration given Kinetic Energy of Rotating Body using this online evaluator? To use this online evaluator for Radius of Gyration given Kinetic Energy of Rotating Body, enter Kinetic Energy Absorbed by Brake (KE), Mass of Brake Assembly (m), Initial Angular Velocity of Braked System (ω₁) & Final Angular Velocity of Braked System (ω₂) and hit the calculate button.

FAQs on Radius of Gyration given Kinetic Energy of Rotating Body

What is the formula to find Radius of Gyration given Kinetic Energy of Rotating Body?

The formula of Radius of Gyration given Kinetic Energy of Rotating Body is expressed as Radius of Gyration of Braked System = sqrt(2*Kinetic Energy Absorbed by Brake/(Mass of Brake Assembly*(Initial Angular Velocity of Braked System^2-Final Angular Velocity of Braked System^2))). Here is an example- 353747.2 = sqrt(2*94950/(1130*(36.65^2-0.52^2))).

How to calculate Radius of Gyration given Kinetic Energy of Rotating Body?

With Kinetic Energy Absorbed by Brake (KE), Mass of Brake Assembly (m), Initial Angular Velocity of Braked System (ω₁) & Final Angular Velocity of Braked System (ω₂) we can find Radius of Gyration given Kinetic Energy of Rotating Body using the formula - Radius of Gyration of Braked System = sqrt(2*Kinetic Energy Absorbed by Brake/(Mass of Brake Assembly*(Initial Angular Velocity of Braked System^2-Final Angular Velocity of Braked System^2))). This formula also uses Square Root (sqrt) function(s).

Can the Radius of Gyration given Kinetic Energy of Rotating Body be negative?

No, the Radius of Gyration given Kinetic Energy of Rotating Body, measured in Length cannot be negative.

Which unit is used to measure Radius of Gyration given Kinetic Energy of Rotating Body?

Radius of Gyration given Kinetic Energy of Rotating Body is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Gyration given Kinetic Energy of Rotating Body can be measured.

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Radius of Gyration given Kinetic Energy of Rotating Body Formula

Radius of Gyration given Kinetic Energy of Rotating Body Example

Radius of Gyration given Kinetic Energy of Rotating Body Solution

Radius of Gyration given Kinetic Energy of Rotating Body Formula Elements

Other formulas in Energy and Thermal Equation category

How to Evaluate Radius of Gyration given Kinetic Energy of Rotating Body?

FAQs on Radius of Gyration given Kinetic Energy of Rotating Body

Variable Name