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Mass of the System When Kinetic Energy of Rotating Body is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
mass = 2*Kinetic Energy Absorbed/((Initial angular velocity^2-Final angular velocity^2)*Radius of gyration^2)
m = 2*KE/((ωo^2-ω^2)*kG^2)
This formula uses 4 Variables
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)
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)
Radius of gyration - Radius of gyration or gyradius of a body about an 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. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Kinetic Energy Absorbed: 10 Joule --> 10 Joule 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
Radius of gyration: 3 Meter --> 3 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
m = 2*KE/((ωo^2-ω^2)*kG^2) --> 2*10/((12^2-48^2)*3^2)
Evaluating ... ...
m = -0.00102880658436214
STEP 3: Convert Result to Output's Unit
-0.00102880658436214 Kilogram --> No Conversion Required
FINAL ANSWER
-0.00102880658436214 Kilogram <-- Mass
(Calculation completed in 00.024 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

Mass of the System When Kinetic Energy of Rotating Body is Given Formula

mass = 2*Kinetic Energy Absorbed/((Initial angular velocity^2-Final angular velocity^2)*Radius of gyration^2)
m = 2*KE/((ωo^2-ω^2)*kG^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 Mass of the System When Kinetic Energy of Rotating Body is Given?

Mass of the System When Kinetic Energy of Rotating Body is Given calculator uses mass = 2*Kinetic Energy Absorbed/((Initial angular velocity^2-Final angular velocity^2)*Radius of gyration^2) to calculate the Mass, The Mass of the System When Kinetic Energy of Rotating Body is Given formula is defined as the measure of its resistance to acceleration when a net force is applied. Mass and is denoted by m symbol.

How to calculate Mass of the System When Kinetic Energy of Rotating Body is Given using this online calculator? To use this online calculator for Mass of the System When Kinetic Energy of Rotating Body is Given, enter Kinetic Energy Absorbed (KE), Initial angular velocity o), Final angular velocity (ω) and Radius of gyration (kG) and hit the calculate button. Here is how the Mass of the System When Kinetic Energy of Rotating Body is Given calculation can be explained with given input values -> -0.001029 = 2*10/((12^2-48^2)*3^2).

FAQ

What is Mass of the System When Kinetic Energy of Rotating Body is Given?
The Mass of the System When Kinetic Energy of Rotating Body is Given formula is defined as the measure of its resistance to acceleration when a net force is applied and is represented as m = 2*KE/((ωo^2-ω^2)*kG^2) or mass = 2*Kinetic Energy Absorbed/((Initial angular velocity^2-Final angular velocity^2)*Radius of gyration^2). Kinetic Energy Absorbed is defined as the maximum difference between initial and final kinetic energies of the system, Initial angular velocity is the velocity at which motion starts, Final angular velocity of the particle and Radius of gyration or gyradius of a body about an 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 Mass of the System When Kinetic Energy of Rotating Body is Given?
The Mass of the System When Kinetic Energy of Rotating Body is Given formula is defined as the measure of its resistance to acceleration when a net force is applied is calculated using mass = 2*Kinetic Energy Absorbed/((Initial angular velocity^2-Final angular velocity^2)*Radius of gyration^2). To calculate Mass of the System When Kinetic Energy of Rotating Body is Given, you need Kinetic Energy Absorbed (KE), Initial angular velocity o), Final angular velocity (ω) and Radius of gyration (kG). With our tool, you need to enter the respective value for Kinetic Energy Absorbed, Initial angular velocity, Final angular velocity and Radius of gyration 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 Mass?
In this formula, Mass uses Kinetic Energy Absorbed, Initial angular velocity, Final angular velocity and Radius of gyration. 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 Mass of the System When Kinetic Energy of Rotating Body is Given calculator used?
Among many, Mass of the System 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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