Initial Angular Velocity of Body 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%
✖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 Braked Assembly [I]			+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%

✖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 Body given Kinetic Energy of Rotating Body [ω₁]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
ω₁ = sqrt((2*KE/I)+ω₂^2)
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

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.
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
Moment of Inertia of Braked Assembly: 141.4 Kilogram Square Meter --> 141.4 Kilogram Square Meter 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

ω₁ = sqrt((2*KE/I)+ω₂^2) --> sqrt((2*94950/141.4)+0.52^2)

Evaluating ... ...

ω₁ = 36.6506341769531

STEP 3: Convert Result to Output's Unit

36.6506341769531 Radian per Second --> No Conversion Required

FINAL ANSWER

36.6506341769531 ≈ 36.65063 Radian per Second <-- Initial Angular Velocity of Braked System

(Calculation completed in 00.004 seconds)

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Home » Physics » Design of Automobile Elements » Design of Brakes » Mechanical » Energy and Thermal Equation » Initial Angular Velocity of Body given Kinetic Energy of Rotating Body

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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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

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

LaTeX 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)
ω₁ = sqrt((2*KE/I)+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 Initial Angular Velocity of Body given Kinetic Energy of Rotating Body?

Initial Angular Velocity of Body given Kinetic Energy of Rotating Body calculator uses 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) to calculate the Initial Angular Velocity of Braked System, The Initial Angular Velocity of Body given Kinetic Energy of Rotating Body formula is defined as angular velocity of system when system is at time T= 0. Initial Angular Velocity of Braked System is denoted by ω₁ symbol.

How to calculate Initial Angular Velocity of Body given Kinetic Energy of Rotating Body using this online calculator? To use this online calculator for Initial Angular Velocity of Body given Kinetic Energy of Rotating Body, enter Kinetic Energy Absorbed by Brake (KE), Moment of Inertia of Braked Assembly (I) & Final Angular Velocity of Braked System (ω₂) and hit the calculate button. Here is how the Initial Angular Velocity of Body given Kinetic Energy of Rotating Body calculation can be explained with given input values -> 36.65063 = sqrt((2*94950/141.4)+0.52^2).

FAQ

What is Initial Angular Velocity of Body given Kinetic Energy of Rotating Body?

The Initial Angular Velocity of Body given Kinetic Energy of Rotating Body formula is defined as angular velocity of system when system is at time T= 0 and is represented as ω₁ = sqrt((2*KE/I)+ω₂^2) or 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). 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 & 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 Initial Angular Velocity of Body given Kinetic Energy of Rotating Body?

The Initial Angular Velocity of Body given Kinetic Energy of Rotating Body formula is defined as angular velocity of system when system is at time T= 0 is calculated using 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). To calculate Initial Angular Velocity of Body given Kinetic Energy of Rotating Body, you need Kinetic Energy Absorbed by Brake (KE), Moment of Inertia of Braked Assembly (I) & Final Angular Velocity of Braked System (ω₂). With our tool, you need to enter the respective value for Kinetic Energy Absorbed by Brake, Moment of Inertia of Braked Assembly & 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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