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## Credits

Osmania University (OU), Hyderabad
Kethavath Srinath has created this Calculator and 500+ more calculators!
Vishwakarma Government Engineering College (VGEC), Ahmedabad
Urvi Rathod has verified this Calculator and 1000+ more calculators!

## Kinetic energy of a Rotating Body Solution

STEP 0: Pre-Calculation Summary
Formula Used
kinetic_energy_absorbed = Moment of Inertia*(Initial angular velocity^2-Final angular velocity^2)/2
KE = I*(ωo^2-ω^2)/2
This formula uses 3 Variables
Variables Used
Moment of Inertia - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis. (Measured in Kilogram Meter²)
Initial angular velocity - Initial angular velocity is the velocity at which motion starts. (Measured in Radian per Second)
Final angular velocity - Final angular velocity of the particle. (Measured in Radian per Second)
STEP 1: Convert Input(s) to Base Unit
Moment of Inertia: 1.125 Kilogram Meter² --> 1.125 Kilogram Meter² No Conversion Required
Initial angular velocity: 12 Radian per Second --> 12 Radian per Second No Conversion Required
Final angular velocity: 48 Radian per Second --> 48 Radian per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
KE = I*(ωo^2-ω^2)/2 --> 1.125*(12^2-48^2)/2
Evaluating ... ...
KE = -1215
STEP 3: Convert Result to Output's Unit
-1215 Joule --> No Conversion Required
FINAL ANSWER
-1215 Joule <-- Kinetic Energy Absorbed
(Calculation completed in 00.007 seconds)

## < 10+ Design of Brakes Calculators

Radius of Gyration When Kinetic Energy of the Rotating Body is Given
radius_of_gyration = sqrt(2*Kinetic Energy Absorbed/(Mass*(Final angular velocity^2-Initial angular velocity^2))) Go
Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given
final_angular_velocity_radpersec = sqrt(Initial angular velocity^2-(2*Kinetic Energy Absorbed/Moment of Inertia)) Go
Mass of the System When Kinetic Energy of Rotating Body is Given
mass = 2*Kinetic Energy Absorbed/((Initial angular velocity^2-Final angular velocity^2)*Radius of gyration^2) Go
Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given
initial_angular_velocity = sqrt((2*Kinetic Energy Absorbed/Mass)+Final angular velocity^2) Go
Initial Velocity of the System When Kinetic Energy Absorbed by the Brakes is Given
initial_velocity = sqrt((2*Kinetic Energy Absorbed/Mass)+Final Velocity^2) Go
Final Velocity When Kinetic Energy Absorbed by the Brakes is Given
final_velocity = sqrt(Initial Velocity^2-(2*Kinetic Energy Absorbed/Mass)) Go
Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given
moment_of_inertia = 2*Kinetic Energy Absorbed/(Initial angular velocity^2-Final angular velocity^2) Go
Kinetic energy of a Rotating Body
kinetic_energy_absorbed = Moment of Inertia*(Initial angular velocity^2-Final angular velocity^2)/2 Go
Mass of the System When Kinetic Energy Absorbed by the Brakes is Given
mass = 2*Kinetic Energy Absorbed/(Initial Velocity^2-Final Velocity^2) Go
Kinetic Energy Absorbed by the Brake
kinetic_energy_absorbed = Mass*(Initial Velocity^2-Final Velocity^2)/2 Go

### Kinetic energy of a Rotating Body Formula

kinetic_energy_absorbed = Moment of Inertia*(Initial angular velocity^2-Final angular velocity^2)/2
KE = I*(ωo^2-ω^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 a Rotating Body?

Kinetic energy of a Rotating Body calculator uses kinetic_energy_absorbed = Moment of Inertia*(Initial angular velocity^2-Final angular velocity^2)/2 to calculate the Kinetic Energy Absorbed, The Kinetic energy of a Rotating Body formula is defined as the measure of the work an object can do by the virtue of its motion. Kinetic Energy Absorbed and is denoted by KE symbol.

How to calculate Kinetic energy of a Rotating Body using this online calculator? To use this online calculator for Kinetic energy of a Rotating Body, enter Moment of Inertia (I), Initial angular velocity o) and Final angular velocity (ω) and hit the calculate button. Here is how the Kinetic energy of a Rotating Body calculation can be explained with given input values -> -1215 = 1.125*(12^2-48^2)/2.

### FAQ

What is Kinetic energy of a Rotating Body?
The Kinetic energy of a 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*(ωo^2-ω^2)/2 or kinetic_energy_absorbed = Moment of Inertia*(Initial angular velocity^2-Final angular velocity^2)/2. Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis, Initial angular velocity is the velocity at which motion starts and Final angular velocity of the particle.
How to calculate Kinetic energy of a Rotating Body?
The Kinetic energy of a 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 = Moment of Inertia*(Initial angular velocity^2-Final angular velocity^2)/2. To calculate Kinetic energy of a Rotating Body, you need Moment of Inertia (I), Initial angular velocity o) and Final angular velocity (ω). With our tool, you need to enter the respective value for Moment of Inertia, Initial angular velocity and Final angular velocity 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?
In this formula, Kinetic Energy Absorbed uses Moment of Inertia, Initial angular velocity and Final angular velocity. We can use 10 other way(s) to calculate the same, which is/are as follows -
• kinetic_energy_absorbed = Mass*(Initial Velocity^2-Final Velocity^2)/2
• mass = 2*Kinetic Energy Absorbed/(Initial Velocity^2-Final Velocity^2)
• initial_velocity = sqrt((2*Kinetic Energy Absorbed/Mass)+Final Velocity^2)
• final_velocity = sqrt(Initial Velocity^2-(2*Kinetic Energy Absorbed/Mass))
• kinetic_energy_absorbed = Moment of Inertia*(Initial angular velocity^2-Final angular velocity^2)/2
• moment_of_inertia = 2*Kinetic Energy Absorbed/(Initial angular velocity^2-Final angular velocity^2)
• initial_angular_velocity = sqrt((2*Kinetic Energy Absorbed/Mass)+Final angular velocity^2)
• final_angular_velocity_radpersec = sqrt(Initial angular velocity^2-(2*Kinetic Energy Absorbed/Moment of Inertia))
• radius_of_gyration = sqrt(2*Kinetic Energy Absorbed/(Mass*(Final angular velocity^2-Initial angular velocity^2)))
• mass = 2*Kinetic Energy Absorbed/((Initial angular velocity^2-Final angular velocity^2)*Radius of gyration^2)
Where is the Kinetic energy of a Rotating Body calculator used?
Among many, Kinetic energy of a Rotating Body calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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