Moment of Inertia of System given Kinetic Energy of Rotating Body Calculator

✖Kinetic Energy Absorbed by Brake is defined as the energy absorbed by the braking system.ⓘ Kinetic Energy Absorbed by Brake [KE]			+10% -10%
✖Initial Angular Velocity of Braked System is the velocity at which the system or the object is rotating before the brakes are applied.ⓘ Initial Angular Velocity of Braked System [ω₁]			+10% -10%
✖Final Angular Velocity of Braked System is the velocity at which the system or the object is rotating after the brakes are totally applied.ⓘ Final Angular Velocity of Braked System [ω₂]			+10% -10%

✖Moment of Inertia of Braked Assembly is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia of System given Kinetic Energy of Rotating Body [I]

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Moment of Inertia of System given Kinetic Energy of Rotating Body Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia of Braked Assembly = 2*Kinetic Energy Absorbed by Brake/(Initial Angular Velocity of Braked System^2-Final Angular Velocity of Braked System^2)
I = 2*KE/(ω₁^2-ω₂^2)
This formula uses 4 Variables

Variables Used

Moment of Inertia of Braked Assembly - (Measured in Kilogram Square Meter) - Moment of Inertia of Braked Assembly is the measure of the resistance of a body to angular acceleration about a given axis.
Kinetic Energy Absorbed by Brake - (Measured in Joule) - Kinetic Energy Absorbed by Brake is defined as the energy absorbed by the braking system.
Initial Angular Velocity of Braked System - (Measured in Radian per Second) - Initial Angular Velocity of Braked System is the velocity at which the system or the object is rotating before the brakes are applied.
Final Angular Velocity of Braked System - (Measured in Radian per Second) - Final Angular Velocity of Braked System is the velocity at which the system or the object is rotating after the brakes are totally applied.

STEP 1: Convert Input(s) to Base Unit

Kinetic Energy Absorbed by Brake: 94950 Joule --> 94950 Joule No Conversion Required
Initial Angular Velocity of Braked System: 36.65 Radian per Second --> 36.65 Radian per Second No Conversion Required
Final Angular Velocity of Braked System: 0.52 Radian per Second --> 0.52 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = 2*KE/(ω₁^2-ω₂^2) --> 2*94950/(36.65^2-0.52^2)

Evaluating ... ...

I = 141.404894485812

STEP 3: Convert Result to Output's Unit

141.404894485812 Kilogram Square Meter --> No Conversion Required

FINAL ANSWER

141.404894485812 ≈ 141.4049 Kilogram Square Meter <-- Moment of Inertia of Braked Assembly

(Calculation completed in 00.020 seconds)

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< Energy and Thermal Equation Calculators

Initial Velocity of System given Kinetic Energy Absorbed by Brakes

LaTeX Go Initial Velocity Before Braking = sqrt((2*Kinetic Energy Absorbed by Brake/Mass of Brake Assembly)+Final Velocity After Braking^2)

Final Velocity given Kinetic Energy Absorbed by Brakes

LaTeX Go Final Velocity After Braking = sqrt(Initial Velocity Before Braking^2-(2*Kinetic Energy Absorbed by Brake/Mass of Brake Assembly))

Mass of System given Kinetic Energy Absorbed by Brakes

LaTeX Go Mass of Brake Assembly = 2*Kinetic Energy Absorbed by Brake/(Initial Velocity Before Braking^2-Final Velocity After Braking^2)

Kinetic Energy Absorbed by Brake

LaTeX Go Kinetic Energy Absorbed by Brake = Mass of Brake Assembly*(Initial Velocity Before Braking^2-Final Velocity After Braking^2)/2

Moment of Inertia of System given Kinetic Energy of Rotating Body Formula

LaTeX Go

Moment of Inertia of Braked Assembly = 2*Kinetic Energy Absorbed by Brake/(Initial Angular Velocity of Braked System^2-Final Angular Velocity of Braked System^2)
I = 2*KE/(ω₁^2-ω₂^2)

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 System given Kinetic Energy of Rotating Body?

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

How to calculate Moment of Inertia of System given Kinetic Energy of Rotating Body using this online calculator? To use this online calculator for Moment of Inertia of System given Kinetic Energy of Rotating Body, enter Kinetic Energy Absorbed by Brake (KE), Initial Angular Velocity of Braked System (ω₁) & Final Angular Velocity of Braked System (ω₂) and hit the calculate button. Here is how the Moment of Inertia of System given Kinetic Energy of Rotating Body calculation can be explained with given input values -> 141.4049 = 2*94950/(36.65^2-0.52^2).

FAQ

What is Moment of Inertia of System given Kinetic Energy of Rotating Body?

The Moment of Inertia of System given Kinetic Energy of Rotating Body formula is defined as quantity expressing body's tendency to resist angular acceleration, which is sum of products of mass of each particle in body with square of its distance from axis of rotation and is represented as I = 2*KE/(ω₁^2-ω₂^2) or Moment of Inertia of Braked Assembly = 2*Kinetic Energy Absorbed by Brake/(Initial Angular Velocity of Braked System^2-Final Angular Velocity of Braked System^2). Kinetic Energy Absorbed by Brake is defined as the energy absorbed by the braking system, Initial Angular Velocity of Braked System is the velocity at which the system or the object is rotating before the brakes are applied & Final Angular Velocity of Braked System is the velocity at which the system or the object is rotating after the brakes are totally applied.

How to calculate Moment of Inertia of System given Kinetic Energy of Rotating Body?

The Moment of Inertia of System given Kinetic Energy of Rotating Body formula is defined as quantity expressing body's tendency to resist angular acceleration, which is sum of products of mass of each particle in body with square of its distance from axis of rotation is calculated using Moment of Inertia of Braked Assembly = 2*Kinetic Energy Absorbed by Brake/(Initial Angular Velocity of Braked System^2-Final Angular Velocity of Braked System^2). To calculate Moment of Inertia of System given Kinetic Energy of Rotating Body, you need Kinetic Energy Absorbed by Brake (KE), Initial Angular Velocity of Braked System (ω₁) & Final Angular Velocity of Braked System (ω₂). With our tool, you need to enter the respective value for Kinetic Energy Absorbed by Brake, Initial Angular Velocity of Braked System & Final Angular Velocity of Braked System and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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