Kinetic energy of Rotating Body Calculator

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✖Moment of Inertia of braked assembly is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia of braked assembly [I]			+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%

✖Kinetic energy absorbed by brake is defined as the energy absorbed by the braking system.ⓘ Kinetic energy of Rotating Body [KE]

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Formula

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Kinetic energy of Rotating Body

Formula

`"KE" = "I"*("ω"_{"1"}^2-"ω"_{"2"}^2)/2`

Example

`"94946.71J"="141.4kg·m²"*(("36.65rad/s")^2-("0.52rad/s")^2)/2`

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Kinetic energy of Rotating Body Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
KE = I*(ω₁^2-ω₂^2)/2
This formula uses 4 Variables

Variables Used

Kinetic energy absorbed by brake - (Measured in Joule) - Kinetic energy absorbed by brake is defined as the energy absorbed by the braking system.
Moment of Inertia of braked assembly - (Measured in Kilogram Square Meter) - Moment of Inertia of braked assembly is the measure of the resistance of a body to angular acceleration about a given axis.
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

Moment of Inertia of braked assembly: 141.4 Kilogram Square Meter --> 141.4 Kilogram Square Meter 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

KE = I*(ω₁^2-ω₂^2)/2 --> 141.4*(36.65^2-0.52^2)/2

Evaluating ... ...

KE = 94946.71347

STEP 3: Convert Result to Output's Unit

94946.71347 Joule --> No Conversion Required

FINAL ANSWER

94946.71347 ≈ 94946.71 Joule <-- Kinetic energy absorbed by brake

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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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

Kinetic energy of Rotating Body Formula

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
KE = I*(ω₁^2-ω₂^2)/2

Define Kinetic Energy?

To accelerate an object we have to apply force. To apply force, we need to do work. When work is done on an object, energy is transferred and the object moves with a new constant speed. The energy that is transferred is known as kinetic energy and it depends on the mass and speed achieved.

How to Calculate Kinetic energy of Rotating Body?

Kinetic energy of Rotating Body calculator uses 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 to calculate the Kinetic energy absorbed by brake, The Kinetic energy of Rotating Body formula is defined as the measure of the work an object can do by the virtue of its motion. Kinetic energy absorbed by brake is denoted by KE symbol.

How to calculate Kinetic energy of Rotating Body using this online calculator? To use this online calculator for Kinetic energy of Rotating Body, enter Moment of Inertia of braked assembly (I), Initial angular velocity of braked system (ω₁) & Final angular velocity of braked system (ω₂) and hit the calculate button. Here is how the Kinetic energy of Rotating Body calculation can be explained with given input values -> 94946.71 = 141.4*(36.65^2-0.52^2)/2.

FAQ

What is Kinetic energy of Rotating Body?

The Kinetic energy of Rotating Body formula is defined as the measure of the work an object can do by the virtue of its motion and is represented as KE = I*(ω₁^2-ω₂^2)/2 or 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. Moment of Inertia of braked assembly is the measure of the resistance of a body to angular acceleration about a given axis, 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 Kinetic energy of Rotating Body?

The Kinetic energy of Rotating Body formula is defined as the measure of the work an object can do by the virtue of its motion is calculated using 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. To calculate Kinetic energy of Rotating Body, you need Moment of Inertia of braked assembly (I), 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 Moment of Inertia of braked 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.

How many ways are there to calculate Kinetic energy absorbed by brake?

In this formula, Kinetic energy absorbed by brake uses Moment of Inertia of braked assembly, Initial angular velocity of braked system & Final angular velocity of braked system. We can use 2 other way(s) to calculate the same, which is/are as follows -

Kinetic energy absorbed by brake = Mass of Brake Assembly*(Initial velocity before braking^2-Final velocity after braking^2)/2
Kinetic energy absorbed by brake = Braking Torque on System*Angle of rotation of brake disc

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