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Radius of Gyration When Kinetic Energy of the Rotating Body is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
radius_of_gyration = sqrt(2*Kinetic Energy Absorbed/(Mass*(Final angular velocity^2-Initial angular velocity^2)))
kG = sqrt(2*KE/(m*(ω^2-ωo^2)))
This formula uses 1 Functions, 4 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)
Initial angular velocity - Initial angular velocity is the velocity at which motion starts. (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
Initial angular velocity: 12 Radian per Second --> 12 Radian per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
kG = sqrt(2*KE/(m*(ω^2-ωo^2))) --> sqrt(2*10/(35.45*(48^2-12^2)))
Evaluating ... ...
kG = 0.0161614380751254
STEP 3: Convert Result to Output's Unit
0.0161614380751254 Meter --> No Conversion Required
FINAL ANSWER
0.0161614380751254 Meter <-- Radius of gyration
(Calculation completed in 00.016 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

Radius of Gyration When Kinetic Energy of the Rotating Body is Given Formula

radius_of_gyration = sqrt(2*Kinetic Energy Absorbed/(Mass*(Final angular velocity^2-Initial angular velocity^2)))
kG = sqrt(2*KE/(m*(ω^2-ωo^2)))

Define Radius of Gyration?

Radius of gyration or gyradius of a body about the 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 Radius of Gyration When Kinetic Energy of the Rotating Body is Given?

Radius of Gyration When Kinetic Energy of the Rotating Body is Given calculator uses radius_of_gyration = sqrt(2*Kinetic Energy Absorbed/(Mass*(Final angular velocity^2-Initial angular velocity^2))) to calculate the Radius of gyration, The Radius of Gyration When Kinetic Energy of the Rotating Body is Given formula 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. Radius of gyration and is denoted by kG symbol.

How to calculate Radius of Gyration When Kinetic Energy of the Rotating Body is Given using this online calculator? To use this online calculator for Radius of Gyration When Kinetic Energy of the Rotating Body is Given, enter Kinetic Energy Absorbed (KE), Mass (m), Final angular velocity (ω) and Initial angular velocity o) and hit the calculate button. Here is how the Radius of Gyration When Kinetic Energy of the Rotating Body is Given calculation can be explained with given input values -> 0.016161 = sqrt(2*10/(35.45*(48^2-12^2))).

FAQ

What is Radius of Gyration When Kinetic Energy of the Rotating Body is Given?
The Radius of Gyration When Kinetic Energy of the Rotating Body is Given formula 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 and is represented as kG = sqrt(2*KE/(m*(ω^2-ωo^2))) or radius_of_gyration = sqrt(2*Kinetic Energy Absorbed/(Mass*(Final angular velocity^2-Initial 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, Final angular velocity of the particle and Initial angular velocity is the velocity at which motion starts.
How to calculate Radius of Gyration When Kinetic Energy of the Rotating Body is Given?
The Radius of Gyration When Kinetic Energy of the Rotating Body is Given formula 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 is calculated using radius_of_gyration = sqrt(2*Kinetic Energy Absorbed/(Mass*(Final angular velocity^2-Initial angular velocity^2))). To calculate Radius of Gyration When Kinetic Energy of the Rotating Body is Given, you need Kinetic Energy Absorbed (KE), Mass (m), Final angular velocity (ω) and Initial angular velocity o). With our tool, you need to enter the respective value for Kinetic Energy Absorbed, Mass, Final angular velocity and Initial 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 Radius of gyration?
In this formula, Radius of gyration uses Kinetic Energy Absorbed, Mass, Final angular velocity and Initial 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 Radius of Gyration When Kinetic Energy of the Rotating Body is Given calculator used?
Among many, Radius of Gyration 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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