Radius of Gyration given Kinetic Energy of Rotating Body Calculator

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✖Kinetic energy absorbed by brake is defined as the energy absorbed by the braking system.ⓘ Kinetic energy absorbed by brake [KE]			+10% -10%
✖Mass of Brake Assembly is defined as the summation of mass of all the objects present in the system on which brakes are applied.ⓘ Mass of Brake Assembly [m]			+10% -10%
✖Initial angular velocity of braked system is the velocity at which the system or the object is rotating before the brakes are applied.ⓘ Initial angular velocity of braked system [ω₁]			+10% -10%
✖Final angular velocity of braked system is the velocity at which the system or the object is rotating after the brakes are totally applied.ⓘ Final angular velocity of braked system [ω₂]			+10% -10%

✖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.ⓘ Radius of Gyration given Kinetic Energy of Rotating Body [k_G]

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Formula

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Radius of Gyration given Kinetic Energy of Rotating Body

Formula

`"k"_{"G"} = sqrt(2*"KE"/("m"*(("ω"_{"1"}^2)-("ω"_{"2"}^2))))`

Example

`"353.7472mm"=sqrt(2*"94950J"/("1130kg"*((("36.65rad/s")^2)-(("0.52rad/s")^2))))`

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Radius of Gyration given Kinetic Energy of Rotating Body Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
k_G = sqrt(2*KE/(m*((ω₁^2)-(ω₂^2))))
This formula uses 1 Functions, 5 Variables

Functions Used

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., sqrt(Number)

Variables Used

Radius of Gyration of braked system - (Measured in Meter) - 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.
Kinetic energy absorbed by brake - (Measured in Joule) - Kinetic energy absorbed by brake is defined as the energy absorbed by the braking system.
Mass of Brake Assembly - (Measured in Kilogram) - Mass of Brake Assembly is defined as the summation of mass of all the objects present in the system on which brakes are applied.
Initial angular velocity of braked system - (Measured in Radian per Second) - Initial angular velocity of braked system is the velocity at which the system or the object is rotating before the brakes are applied.
Final angular velocity of braked system - (Measured in Radian per Second) - Final angular velocity of braked system is the velocity at which the system or the object is rotating after the brakes are totally applied.

STEP 1: Convert Input(s) to Base Unit

Kinetic energy absorbed by brake: 94950 Joule --> 94950 Joule No Conversion Required
Mass of Brake Assembly: 1130 Kilogram --> 1130 Kilogram No Conversion Required
Initial angular velocity of braked system: 36.65 Radian per Second --> 36.65 Radian per Second No Conversion Required
Final angular velocity of braked system: 0.52 Radian per Second --> 0.52 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_G = sqrt(2*KE/(m*((ω₁^2)-(ω₂^2)))) --> sqrt(2*94950/(1130*((36.65^2)-(0.52^2))))

Evaluating ... ...

k_G = 0.353747190471113

STEP 3: Convert Result to Output's Unit

0.353747190471113 Meter -->353.747190471113 Millimeter (Check conversion here)

FINAL ANSWER

353.747190471113 ≈ 353.7472 Millimeter <-- Radius of Gyration of braked system

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Brakes » Energy and Thermal Equation » Radius of Gyration given Kinetic Energy of Rotating Body

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 19 Energy and Thermal Equation Calculators

Radius of Gyration given Kinetic Energy of Rotating Body

Go 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))))

Mass of System given Kinetic Energy of Rotating Body

Go Mass of Brake Assembly = 2*Kinetic energy absorbed by brake/((Initial angular velocity of braked system^2-Final angular velocity of braked system^2)*Radius of Gyration of braked system^2)

Initial Angular Velocity of Body given Kinetic Energy of Rotating Body

Go Initial angular velocity of braked system = sqrt((2*Kinetic energy absorbed by brake/Moment of Inertia of braked assembly)+Final angular velocity of braked system^2)

Final Angular Velocity of Body given Kinetic Energy of Rotating Body

Go 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))

Moment of Inertia of System given Kinetic Energy of Rotating Body

Go Moment of Inertia of braked assembly = 2*Kinetic energy absorbed by brake/(Initial angular velocity of braked system^2-Final angular velocity of braked system^2)

Kinetic energy of Rotating Body

Go Kinetic energy absorbed by brake = Moment of Inertia of braked assembly*(Initial angular velocity of braked system^2-Final angular velocity of braked system^2)/2

Initial Velocity of System given Kinetic Energy Absorbed by Brakes

Go Initial velocity before braking = sqrt((2*Kinetic energy absorbed by brake/Mass of Brake Assembly)+Final velocity after braking^2)

Final Velocity given Kinetic Energy Absorbed by Brakes

Go Final velocity after braking = sqrt(Initial velocity before braking^2-(2*Kinetic energy absorbed by brake/Mass of Brake Assembly))

Mass of System given Kinetic Energy Absorbed by Brakes

Go Mass of Brake Assembly = 2*Kinetic energy absorbed by brake/(Initial velocity before braking^2-Final velocity after braking^2)

Kinetic Energy Absorbed by Brake

Go Kinetic energy absorbed by brake = Mass of Brake Assembly*(Initial velocity before braking^2-Final velocity after braking^2)/2

Mass of System given Potential Energy Absorbed during Braking Period

Go Mass of Brake Assembly = Potential energy absorbed during braking/(Acceleration due to Gravity*Change in height of vehicle)

Potential Energy Absorbed during Braking Period

Go Potential energy absorbed during braking = Mass of Brake Assembly*Acceleration due to Gravity*Change in height of vehicle

Specific Heat of Brake Drum Material given Temperature Rise of Brake Drum Assembly

Go Specific Heat of Brake Drum = Total Energy of Brake/(Mass of Brake Assembly*Temperature Change of Brake Assembly)

Mass of Brake Drum Assembly given Temperature Rise of Brake Drum Assembly

Go Mass of Brake Assembly = Total Energy of Brake/(Temperature Change of Brake Assembly*Specific Heat of Brake Drum)

Temperature Rise of Brake Drum Assembly

Go Temperature Change of Brake Assembly = Total Energy of Brake/(Mass of Brake Assembly*Specific Heat of Brake Drum)

Total Energy Absorbed by Brake given Temperature Rise of Brake Drum Assembly

Go Total Energy of Brake = Temperature Change of Brake Assembly*Mass of Brake Assembly*Specific Heat of Brake Drum

Brake Drum Rotational Angle given Work Done by Brake

Go Angle of rotation of brake disc = Kinetic energy absorbed by brake/Braking Torque on System

Braking Torque given Work Done by Brake

Go Braking Torque on System = Kinetic energy absorbed by brake/Angle of rotation of brake disc

Total Energy Absorbed by Brake

Go Kinetic energy absorbed by brake = Braking Torque on System*Angle of rotation of brake disc

Radius of Gyration given Kinetic Energy of Rotating Body Formula

Define Radius of Gyration?

Radius of gyration or gyradius of a body about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there.

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

Radius of Gyration given Kinetic Energy of Rotating Body calculator 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 calculate 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 calculate Radius of Gyration given Kinetic Energy of Rotating Body using this online calculator? To use this online calculator 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. Here is how the Radius of Gyration given Kinetic Energy of Rotating Body calculation can be explained with given input values -> 353747.2 = sqrt(2*94950/(1130*((36.65^2)-(0.52^2)))).

FAQ

What is Radius of Gyration given Kinetic Energy of Rotating Body?

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 and is represented as k_G = sqrt(2*KE/(m*((ω₁^2)-(ω₂^2)))) or 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)))). Kinetic energy absorbed by brake is defined as the energy absorbed by the braking system, Mass of Brake Assembly is defined as the summation of mass of all the objects present in the system on which brakes are applied, Initial angular velocity of braked system is the velocity at which the system or the object is rotating before the brakes are applied & Final angular velocity of braked system is the velocity at which the system or the object is rotating after the brakes are totally applied.

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

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 is calculated using 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 calculate Radius of Gyration given Kinetic Energy of Rotating Body, you need 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). With our tool, you need to enter the respective value for Kinetic energy absorbed by brake, Mass of Brake Assembly, Initial angular velocity of braked system & Final angular velocity of braked system and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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