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Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
moment_of_inertia = 2*Kinetic Energy Absorbed/(Initial angular velocity^2-Final angular velocity^2)
I = 2*KE/(ωo^2-ω^2)
This formula uses 3 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)
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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = 2*KE/(ωo^2-ω^2) --> 2*10/(12^2-48^2)
Evaluating ... ...
I = -0.00925925925925926
STEP 3: Convert Result to Output's Unit
-0.00925925925925926 Kilogram Meter² --> No Conversion Required
FINAL ANSWER
-0.00925925925925926 Kilogram Meter² <-- Moment of Inertia
(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

Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given Formula

moment_of_inertia = 2*Kinetic Energy Absorbed/(Initial angular velocity^2-Final angular velocity^2)
I = 2*KE/(ωo^2-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 Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given?

Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given calculator uses moment_of_inertia = 2*Kinetic Energy Absorbed/(Initial angular velocity^2-Final angular velocity^2) to calculate the Moment of Inertia, The Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given formula is defined as a quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation. Moment of Inertia and is denoted by I symbol.

How to calculate Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given using this online calculator? To use this online calculator for Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given, enter Kinetic Energy Absorbed (KE), Initial angular velocity o) and Final angular velocity (ω) and hit the calculate button. Here is how the Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given calculation can be explained with given input values -> -0.009259 = 2*10/(12^2-48^2).

FAQ

What is Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given?
The Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given formula is defined as a quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation and is represented as I = 2*KE/(ωo^2-ω^2) or moment_of_inertia = 2*Kinetic Energy Absorbed/(Initial angular velocity^2-Final angular velocity^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 and Final angular velocity of the particle.
How to calculate Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given?
The Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given formula is defined as a quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation is calculated using moment_of_inertia = 2*Kinetic Energy Absorbed/(Initial angular velocity^2-Final angular velocity^2). To calculate Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given, you need Kinetic Energy Absorbed (KE), Initial angular velocity o) and Final angular velocity (ω). With our tool, you need to enter the respective value for Kinetic Energy Absorbed, 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 Moment of Inertia?
In this formula, Moment of Inertia uses Kinetic Energy Absorbed, 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 Moment of Inertia of the System When Kinetic Energy of the Rotating Body is Given calculator used?
Among many, Moment of Inertia of the System 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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