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 00.004 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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Vishwakarma Government Engineering College (VGEC), Ahmedabad
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19 Energy and Thermal Equation Calculators

Radius of Gyration given Kinetic Energy of Rotating Body
Go Radius of Gyration of braked system = sqrt(2*Kinetic energy absorbed by brake/(Mass of Brake Assembly*((Initial angular velocity of braked system^2)-(Final angular velocity of braked system^2))))
Mass of System given Kinetic Energy of Rotating Body
Go Mass of Brake Assembly = 2*Kinetic energy absorbed by brake/((Initial angular velocity of braked system^2-Final angular velocity of braked system^2)*Radius of Gyration of braked system^2)
Initial Angular Velocity of Body given Kinetic Energy of Rotating Body
Go Initial angular velocity of braked system = sqrt((2*Kinetic energy absorbed by brake/Moment of Inertia of braked assembly)+Final angular velocity of braked system^2)
Final Angular Velocity of Body given Kinetic Energy of Rotating Body
Go Final angular velocity of braked system = sqrt(Initial angular velocity of braked system^2-(2*Kinetic energy absorbed by brake/Moment of Inertia of braked assembly))
Moment of Inertia of System given Kinetic Energy of Rotating Body
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)
Kinetic energy of Rotating Body
Go Kinetic energy absorbed by brake = Moment of Inertia of braked assembly*(Initial angular velocity of braked system^2-Final angular velocity of braked system^2)/2
Initial Velocity of System given Kinetic Energy Absorbed by Brakes
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
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
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
Go Kinetic energy absorbed by brake = Mass of Brake Assembly*(Initial velocity before braking^2-Final velocity after braking^2)/2
Mass of System given Potential Energy Absorbed during Braking Period
Go Mass of Brake Assembly = Potential energy absorbed during braking/(Acceleration due to Gravity*Change in height of vehicle)
Potential Energy Absorbed during Braking Period
Go Potential energy absorbed during braking = Mass of Brake Assembly*Acceleration due to Gravity*Change in height of vehicle
Specific Heat of Brake Drum Material given Temperature Rise of Brake Drum Assembly
Go Specific Heat of Brake Drum = Total Energy of Brake/(Mass of Brake Assembly*Temperature Change of Brake Assembly)
Mass of Brake Drum Assembly given Temperature Rise of Brake Drum Assembly
Go Mass of Brake Assembly = Total Energy of Brake/(Temperature Change of Brake Assembly*Specific Heat of Brake Drum)
Temperature Rise of Brake Drum Assembly
Go Temperature Change of Brake Assembly = Total Energy of Brake/(Mass of Brake Assembly*Specific Heat of Brake Drum)
Total Energy Absorbed by Brake given Temperature Rise of Brake Drum Assembly
Go Total Energy of Brake = Temperature Change of Brake Assembly*Mass of Brake Assembly*Specific Heat of Brake Drum
Brake Drum Rotational Angle given Work Done by Brake
Go Angle of rotation of brake disc = Kinetic energy absorbed by brake/Braking Torque on System
Braking Torque given Work Done by Brake
Go Braking Torque on System = Kinetic energy absorbed by brake/Angle of rotation of brake disc
Total Energy Absorbed by Brake
Go Kinetic energy absorbed by brake = Braking Torque on System*Angle of rotation of brake disc

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

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 1) & Final angular velocity of braked system 2) 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 1) & Final angular velocity of braked system 2). 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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