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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
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## Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
initial_angular_velocity = sqrt((2*Kinetic Energy Absorbed/Mass)+Final angular velocity^2)
ωo = sqrt((2*KE/m)+ω^2)
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Kinetic Energy Absorbed - Kinetic Energy Absorbed is defined as the maximum difference between initial and final kinetic energies of the system. (Measured in Joule)
Mass - Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it. (Measured in Kilogram)
Final angular velocity - Final angular velocity of the particle. (Measured in Radian per Second)
STEP 1: Convert Input(s) to Base Unit
Kinetic Energy Absorbed: 10 Joule --> 10 Joule No Conversion Required
Mass: 35.45 Kilogram --> 35.45 Kilogram 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
ωo = sqrt((2*KE/m)+ω^2) --> sqrt((2*10/35.45)+48^2)
Evaluating ... ...
ωo = 48.005876462098
STEP 3: Convert Result to Output's Unit
48.005876462098 Radian per Second --> No Conversion Required
FINAL ANSWER
48.005876462098 Radian per Second <-- Initial angular velocity
(Calculation completed in 00.015 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

### Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given Formula

initial_angular_velocity = sqrt((2*Kinetic Energy Absorbed/Mass)+Final angular velocity^2)
ωo = sqrt((2*KE/m)+ω^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 Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given?

Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given calculator uses initial_angular_velocity = sqrt((2*Kinetic Energy Absorbed/Mass)+Final angular velocity^2) to calculate the Initial angular velocity, The Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given formula is defined as the angular velocity of the system when the system is at time T= 0. Initial angular velocity and is denoted by ωo symbol.

How to calculate Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given using this online calculator? To use this online calculator for Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given, enter Kinetic Energy Absorbed (KE), Mass (m) and Final angular velocity (ω) and hit the calculate button. Here is how the Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given calculation can be explained with given input values -> 48.00588 = sqrt((2*10/35.45)+48^2).

### FAQ

What is Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given?
The Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given formula is defined as the angular velocity of the system when the system is at time T= 0 and is represented as ωo = sqrt((2*KE/m)+ω^2) or initial_angular_velocity = sqrt((2*Kinetic Energy Absorbed/Mass)+Final angular velocity^2). Kinetic Energy Absorbed is defined as the maximum difference between initial and final kinetic energies of the system, Mass is the quantity of matter in a body regardless of its volume or of any forces acting on it and Final angular velocity of the particle.
How to calculate Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given?
The Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given formula is defined as the angular velocity of the system when the system is at time T= 0 is calculated using initial_angular_velocity = sqrt((2*Kinetic Energy Absorbed/Mass)+Final angular velocity^2). To calculate Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given, you need Kinetic Energy Absorbed (KE), Mass (m) and Final angular velocity (ω). With our tool, you need to enter the respective value for Kinetic Energy Absorbed, Mass 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 Initial angular velocity?
In this formula, Initial angular velocity uses Kinetic Energy Absorbed, Mass 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 Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given calculator used?
Among many, Initial Angular Velocity of the Body When Kinetic Energy of the Rotating Body is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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