Final Angular Velocity of Body given Kinetic Energy of Rotating Body Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
ω2 = sqrt(ω1^2-(2*KE/I))
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
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.
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.
Kinetic energy absorbed by brake - (Measured in Joule) - Kinetic energy absorbed by brake is defined as the energy absorbed by the braking system.
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.
STEP 1: Convert Input(s) to Base Unit
Initial angular velocity of braked system: 36.65 Radian per Second --> 36.65 Radian per Second No Conversion Required
Kinetic energy absorbed by brake: 94950 Joule --> 94950 Joule No Conversion Required
Moment of Inertia of braked assembly: 141.4 Kilogram Square Meter --> 141.4 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ω2 = sqrt(ω1^2-(2*KE/I)) --> sqrt(36.65^2-(2*94950/141.4))
Evaluating ... ...
ω2 = 0.473195971196757
STEP 3: Convert Result to Output's Unit
0.473195971196757 Radian per Second --> No Conversion Required
FINAL ANSWER
0.473195971196757 0.473196 Radian per Second <-- Final angular velocity of braked system
(Calculation completed in 00.020 seconds)

Credits

Created by Kethavath Srinath
Osmania University (OU), Hyderabad
Kethavath Srinath has created this Calculator and 1000+ more calculators!
Verified by Urvi Rathod
Vishwakarma Government Engineering College (VGEC), Ahmedabad
Urvi Rathod has verified this Calculator and 1900+ more calculators!

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

Final Angular Velocity of Body given Kinetic Energy of Rotating Body Formula

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))
ω2 = sqrt(ω1^2-(2*KE/I))

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 Final Angular Velocity of Body given Kinetic Energy of Rotating Body?

Final Angular Velocity of Body given Kinetic Energy of Rotating Body calculator uses 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)) to calculate the Final angular velocity of braked system, The Final Angular Velocity of Body given Kinetic Energy of Rotating Body formula is defined as angular velocity of rotating body when time T= t. Final angular velocity of braked system is denoted by ω2 symbol.

How to calculate Final Angular Velocity of Body given Kinetic Energy of Rotating Body using this online calculator? To use this online calculator for Final Angular Velocity of Body given Kinetic Energy of Rotating Body, enter Initial angular velocity of braked system 1), Kinetic energy absorbed by brake (KE) & Moment of Inertia of braked assembly (I) and hit the calculate button. Here is how the Final Angular Velocity of Body given Kinetic Energy of Rotating Body calculation can be explained with given input values -> 0.473196 = sqrt(36.65^2-(2*94950/141.4)).

FAQ

What is Final Angular Velocity of Body given Kinetic Energy of Rotating Body?
The Final Angular Velocity of Body given Kinetic Energy of Rotating Body formula is defined as angular velocity of rotating body when time T= t and is represented as ω2 = sqrt(ω1^2-(2*KE/I)) or 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)). Initial angular velocity of braked system is the velocity at which the system or the object is rotating before the brakes are applied, Kinetic energy absorbed by brake is defined as the energy absorbed by the braking system & Moment of Inertia of braked assembly is the measure of the resistance of a body to angular acceleration about a given axis.
How to calculate Final Angular Velocity of Body given Kinetic Energy of Rotating Body?
The Final Angular Velocity of Body given Kinetic Energy of Rotating Body formula is defined as angular velocity of rotating body when time T= t is calculated using 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)). To calculate Final Angular Velocity of Body given Kinetic Energy of Rotating Body, you need Initial angular velocity of braked system 1), Kinetic energy absorbed by brake (KE) & Moment of Inertia of braked assembly (I). With our tool, you need to enter the respective value for Initial angular velocity of braked system, Kinetic energy absorbed by brake & Moment of Inertia of braked assembly and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!