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

STEP 0: Pre-Calculation Summary
Formula Used
final_angular_velocity_radpersec = sqrt(Initial angular velocity^2-(2*Kinetic Energy Absorbed/Moment of Inertia))
ω = sqrt(ωo^2-(2*KE/I))
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Initial angular velocity - Initial angular velocity is the velocity at which motion starts. (Measured in Radian per Second)
Kinetic Energy Absorbed - Kinetic Energy Absorbed is defined as the maximum difference between initial and final kinetic energies of the system. (Measured in Joule)
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)
STEP 1: Convert Input(s) to Base Unit
Initial angular velocity: 12 Radian per Second --> 12 Radian per Second No Conversion Required
Kinetic Energy Absorbed: 10 Joule --> 10 Joule No Conversion Required
Moment of Inertia: 1.125 Kilogram Meter² --> 1.125 Kilogram Meter² No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ω = sqrt(ωo^2-(2*KE/I)) --> sqrt(12^2-(2*10/1.125))
Evaluating ... ...
ω = 11.2348663642351
STEP 3: Convert Result to Output's Unit
11.2348663642351 Radian per Second --> No Conversion Required
FINAL ANSWER
11.2348663642351 Radian per Second <-- Final angular velocity
(Calculation completed in 00.010 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

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

final_angular_velocity_radpersec = sqrt(Initial angular velocity^2-(2*Kinetic Energy Absorbed/Moment of Inertia))
ω = sqrt(ωo^2-(2*KE/I))

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 Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given?

Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given calculator uses final_angular_velocity_radpersec = sqrt(Initial angular velocity^2-(2*Kinetic Energy Absorbed/Moment of Inertia)) to calculate the Final angular velocity, The Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given formula is defined as the angular velocity of the rotating body when the time T= t. Final angular velocity and is denoted by ω symbol.

How to calculate Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given using this online calculator? To use this online calculator for Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given, enter Initial angular velocity o), Kinetic Energy Absorbed (KE) and Moment of Inertia (I) and hit the calculate button. Here is how the Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given calculation can be explained with given input values -> 11.23487 = sqrt(12^2-(2*10/1.125)).

FAQ

What is Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given?
The Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given formula is defined as the angular velocity of the rotating body when the time T= t and is represented as ω = sqrt(ωo^2-(2*KE/I)) or final_angular_velocity_radpersec = sqrt(Initial angular velocity^2-(2*Kinetic Energy Absorbed/Moment of Inertia)). Initial angular velocity is the velocity at which motion starts, Kinetic Energy Absorbed is defined as the maximum difference between initial and final kinetic energies of the system and Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
How to calculate Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given?
The Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given formula is defined as the angular velocity of the rotating body when the time T= t is calculated using final_angular_velocity_radpersec = sqrt(Initial angular velocity^2-(2*Kinetic Energy Absorbed/Moment of Inertia)). To calculate Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given, you need Initial angular velocity o), Kinetic Energy Absorbed (KE) and Moment of Inertia (I). With our tool, you need to enter the respective value for Initial angular velocity, Kinetic Energy Absorbed and Moment of Inertia 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 Final angular velocity?
In this formula, Final angular velocity uses Initial angular velocity, Kinetic Energy Absorbed and Moment of Inertia. 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 Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given calculator used?
Among many, Final Angular Velocity of the Body When Kinetic Energy of Rotating Body is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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