Kinetic Energy given Angular Velocity Calculator

✖Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it.ⓘ Mass 1 [m₁]			+10% -10%
✖Radius of mass 1 is a distance of mass 1 from the center of mass.ⓘ Radius of Mass 1 [R₁]			+10% -10%
✖Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it.ⓘ Mass 2 [m₂]			+10% -10%
✖Radius of Mass 2 is a distance of mass 2 from the center of mass.ⓘ Radius of Mass 2 [R₂]			+10% -10%
✖Angular Velocity Spectroscopy refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.ⓘ Angular Velocity Spectroscopy [ω]			+10% -10%

✖Kinetic Energy given Angular Momentum as the work needed to accelerate a body of a given mass from rest to its stated velocity.ⓘ Kinetic Energy given Angular Velocity [KE1]

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Kinetic Energy given Angular Velocity

Formula

`"KE1" = (("m"_{"1"}*("R"_{"1"}^2))+("m"_{"2"}*("R"_{"2"}^2)))*("ω"^2)/2`

Example

`"3.51J"=(("14kg"*(("1.5cm")^2))+("16kg"*(("3cm")^2)))*(("20rad/s")^2)/2`

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Kinetic Energy given Angular Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Kinetic Energy given Angular Momentum = ((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2)))*(Angular Velocity Spectroscopy^2)/2
KE1 = ((m₁*(R₁^2))+(m₂*(R₂^2)))*(ω^2)/2
This formula uses 6 Variables

Variables Used

Kinetic Energy given Angular Momentum - (Measured in Joule) - Kinetic Energy given Angular Momentum as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Mass 1 - (Measured in Kilogram) - Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it.
Radius of Mass 1 - (Measured in Meter) - Radius of mass 1 is a distance of mass 1 from the center of mass.
Mass 2 - (Measured in Kilogram) - Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it.
Radius of Mass 2 - (Measured in Meter) - Radius of Mass 2 is a distance of mass 2 from the center of mass.
Angular Velocity Spectroscopy - (Measured in Radian per Second) - Angular Velocity Spectroscopy refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.

STEP 1: Convert Input(s) to Base Unit

Mass 1: 14 Kilogram --> 14 Kilogram No Conversion Required
Radius of Mass 1: 1.5 Centimeter --> 0.015 Meter (Check conversion here)
Mass 2: 16 Kilogram --> 16 Kilogram No Conversion Required
Radius of Mass 2: 3 Centimeter --> 0.03 Meter (Check conversion here)
Angular Velocity Spectroscopy: 20 Radian per Second --> 20 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

KE1 = ((m₁*(R₁^2))+(m₂*(R₂^2)))*(ω^2)/2 --> ((14*(0.015^2))+(16*(0.03^2)))*(20^2)/2

Evaluating ... ...

KE1 = 3.51

STEP 3: Convert Result to Output's Unit

3.51 Joule --> No Conversion Required

FINAL ANSWER

3.51 Joule <-- Kinetic Energy given Angular Momentum

(Calculation completed in 00.004 seconds)

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Created by Nishant Sihag

Indian Institute of Technology (IIT), Delhi

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National Institute of Information Technology (NIIT), Neemrana

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< 8 Kinetic Energy for System Calculators

Kinetic Energy given Angular Velocity

Go Kinetic Energy given Angular Momentum = ((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2)))*(Angular Velocity Spectroscopy^2)/2

Velocity of Particle 1 given Kinetic Energy

Go Velocity of Particle with Mass m1 = sqrt(((2*Kinetic Energy)-(Mass 2*Velocity of Particle with Mass m2^2))/Mass 1)

Velocity of Particle 2 given Kinetic Energy

Go Velocity of Particle with Mass m2 = sqrt(((2*Kinetic Energy)-(Mass 1*Velocity of Particle with Mass m1^2))/Mass 2)

Kinetic Energy of System

Go Kinetic Energy = ((Mass 1*(Velocity of Particle with Mass m1^2))+(Mass 2*(Velocity of Particle with Mass m2^2)))/2

Velocity of Particle 2

Go Velocity of Particle with Mass m2 = 2*pi*Radius of Mass 2*Rotational Frequency

Kinetic Energy given Inertia and Angular Velocity

Go Kinetic Energy given Inertia and Angular Velocity = Moment of Inertia*(Angular Velocity Spectroscopy^2)/2

Velocity of Particle 1

Go Velocity of Particle 1 = 2*pi*Radius of Mass 1*Rotational Frequency

Kinetic Energy given Angular Momentum

Go Kinetic Energy given Angular Momentum = (Angular Momentum/2)/(2*Moment of Inertia)

< 8 Kinetic Energy of System Calculators

Kinetic Energy given Angular Velocity

Go Kinetic Energy given Angular Momentum = ((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2)))*(Angular Velocity Spectroscopy^2)/2

Velocity of Particle 1 given Kinetic Energy

Go Velocity of Particle with Mass m1 = sqrt(((2*Kinetic Energy)-(Mass 2*Velocity of Particle with Mass m2^2))/Mass 1)

Velocity of Particle 2 given Kinetic Energy

Go Velocity of Particle with Mass m2 = sqrt(((2*Kinetic Energy)-(Mass 1*Velocity of Particle with Mass m1^2))/Mass 2)

Kinetic Energy of System

Go Kinetic Energy = ((Mass 1*(Velocity of Particle with Mass m1^2))+(Mass 2*(Velocity of Particle with Mass m2^2)))/2

Velocity of Particle 2

Go Velocity of Particle with Mass m2 = 2*pi*Radius of Mass 2*Rotational Frequency

Kinetic Energy given Inertia and Angular Velocity

Go Kinetic Energy given Inertia and Angular Velocity = Moment of Inertia*(Angular Velocity Spectroscopy^2)/2

Velocity of Particle 1

Go Velocity of Particle 1 = 2*pi*Radius of Mass 1*Rotational Frequency

Kinetic Energy given Angular Momentum

Go Kinetic Energy given Angular Momentum = (Angular Momentum/2)/(2*Moment of Inertia)

Kinetic Energy given Angular Velocity Formula

Kinetic Energy given Angular Momentum = ((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2)))*(Angular Velocity Spectroscopy^2)/2
KE1 = ((m₁*(R₁^2))+(m₂*(R₂^2)))*(ω^2)/2

How to get Kinetic energy(KE) when angular velocity is given?

Kinetic energy is the work needed to accelerate a body of a given mass from rest to its stated velocity. Which is numerically written as half*mass *square of velocity for a given object. So for a system we have to add kinetic energy of the individual masses. Thus we get total Kinetic energy of system. Now we further substitute velocity by (radius*angular velocity). And obtain a relation of kinetic energy in terms of angular velocity(ω).

How to Calculate Kinetic Energy given Angular Velocity?

Kinetic Energy given Angular Velocity calculator uses Kinetic Energy given Angular Momentum = ((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2)))*(Angular Velocity Spectroscopy^2)/2 to calculate the Kinetic Energy given Angular Momentum, The Kinetic energy given angular velocity formula is defined as the sum of the kinetic energy for each mass. Linear velocity(v) is radius(r) times angular velocity (ω). So kinetic energy formula can be modified by substituting v by r*ω. Thus we obtain total kinetic energy in terms of angular velocity(ω). Kinetic Energy given Angular Momentum is denoted by KE1 symbol.

How to calculate Kinetic Energy given Angular Velocity using this online calculator? To use this online calculator for Kinetic Energy given Angular Velocity, enter Mass 1 (m₁), Radius of Mass 1 (R₁), Mass 2 (m₂), Radius of Mass 2 (R₂) & Angular Velocity Spectroscopy (ω) and hit the calculate button. Here is how the Kinetic Energy given Angular Velocity calculation can be explained with given input values -> 3.51 = ((14*(0.015^2))+(16*(0.03^2)))*(20^2)/2.

FAQ

What is Kinetic Energy given Angular Velocity?

The Kinetic energy given angular velocity formula is defined as the sum of the kinetic energy for each mass. Linear velocity(v) is radius(r) times angular velocity (ω). So kinetic energy formula can be modified by substituting v by r*ω. Thus we obtain total kinetic energy in terms of angular velocity(ω) and is represented as KE1 = ((m₁*(R₁^2))+(m₂*(R₂^2)))*(ω^2)/2 or Kinetic Energy given Angular Momentum = ((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2)))*(Angular Velocity Spectroscopy^2)/2. Mass 1 is the quantity of matter in a body 1 regardless of its volume or of any forces acting on it, Radius of mass 1 is a distance of mass 1 from the center of mass, Mass 2 is the quantity of matter in a body 2 regardless of its volume or of any forces acting on it, Radius of Mass 2 is a distance of mass 2 from the center of mass & Angular Velocity Spectroscopy refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.

How to calculate Kinetic Energy given Angular Velocity?

The Kinetic energy given angular velocity formula is defined as the sum of the kinetic energy for each mass. Linear velocity(v) is radius(r) times angular velocity (ω). So kinetic energy formula can be modified by substituting v by r*ω. Thus we obtain total kinetic energy in terms of angular velocity(ω) is calculated using Kinetic Energy given Angular Momentum = ((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2)))*(Angular Velocity Spectroscopy^2)/2. To calculate Kinetic Energy given Angular Velocity, you need Mass 1 (m₁), Radius of Mass 1 (R₁), Mass 2 (m₂), Radius of Mass 2 (R₂) & Angular Velocity Spectroscopy (ω). With our tool, you need to enter the respective value for Mass 1, Radius of Mass 1, Mass 2, Radius of Mass 2 & Angular Velocity Spectroscopy 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 Kinetic Energy given Angular Momentum?

In this formula, Kinetic Energy given Angular Momentum uses Mass 1, Radius of Mass 1, Mass 2, Radius of Mass 2 & Angular Velocity Spectroscopy. We can use 2 other way(s) to calculate the same, which is/are as follows -

Kinetic Energy given Angular Momentum = (Angular Momentum/2)/(2*Moment of Inertia)
Kinetic Energy given Angular Momentum = (Angular Momentum/2)/(2*Moment of Inertia)

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