Angular Velocity given Inertia and Kinetic Energy Calculator

✖Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.ⓘ Kinetic Energy [KE]			+10% -10%
✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia [I]			+10% -10%

✖Angular Velocity given Momentum and Inertia refers to how fast an object rotates or revolves relative to another point.ⓘ Angular Velocity given Inertia and Kinetic Energy [ω2]

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Formula

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Angular Velocity given Inertia and Kinetic Energy

Formula

`"ω2" = sqrt(2*"KE"/"I")`

Example

`"8.43274rad/s"=sqrt(2*"40J"/"1.125kg·m²")`

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Download Angular Momentum and Velocity of Diatomic Molecule Formulas PDF

Angular Velocity given Inertia and Kinetic Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Velocity given Momentum and Inertia = sqrt(2*Kinetic Energy/Moment of Inertia)
ω2 = sqrt(2*KE/I)
This formula uses 1 Functions, 3 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

Angular Velocity given Momentum and Inertia - (Measured in Radian per Second) - Angular Velocity given Momentum and Inertia refers to how fast an object rotates or revolves relative to another point.
Kinetic Energy - (Measured in Joule) - Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

STEP 1: Convert Input(s) to Base Unit

Kinetic Energy: 40 Joule --> 40 Joule No Conversion Required
Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω2 = sqrt(2*KE/I) --> sqrt(2*40/1.125)

Evaluating ... ...

ω2 = 8.43274042711568

STEP 3: Convert Result to Output's Unit

8.43274042711568 Radian per Second --> No Conversion Required

FINAL ANSWER

8.43274042711568 ≈ 8.43274 Radian per Second <-- Angular Velocity given Momentum and Inertia

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Analytical chemistry » Molecular Spectroscopy » Rotational Spectroscopy » Angular Momentum and Velocity of Diatomic Molecule » Angular Velocity given Inertia and Kinetic Energy

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Indian Institute of Technology (IIT), Delhi

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< 9 Angular Momentum and Velocity of Diatomic Molecule Calculators

Angular Velocity given Kinetic Energy

Go Angular Velocity of Diatomic Molecule = sqrt(2*Kinetic Energy/((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2))))

Angular Velocity given Inertia and Kinetic Energy

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

Rotational Frequency given Velocity of Particle 1

Go Rotational Frequency = Velocity of Particle with Mass m1/(2*pi*Radius of Mass 1)

Rotational Frequency given Velocity of Particle 2

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

Angular Momentum given Moment of Inertia

Go Angular Momentum given Moment of Inertia = Moment of Inertia*Angular Velocity Spectroscopy

Angular Momentum given Kinetic Energy

Go Angular Momentum1 = sqrt(2*Moment of Inertia*Kinetic Energy)

Rotational Frequency given Angular Frequency

Go Rotational Frequency given Angular Frequency = Angular Velocity Spectroscopy/(2*pi)

Angular Velocity given Angular Momentum and Inertia

Go Angular Velocity given Momentum and Inertia = Angular Momentum/Moment of Inertia

Angular Velocity of Diatomic Molecule

Go Angular Velocity of Diatomic Molecule = 2*pi*Rotational Frequency

< 9 Angular momentum and velocity of diatomic molecule Calculators

Angular Velocity given Kinetic Energy

Go Angular Velocity of Diatomic Molecule = sqrt(2*Kinetic Energy/((Mass 1*(Radius of Mass 1^2))+(Mass 2*(Radius of Mass 2^2))))

Angular Velocity given Inertia and Kinetic Energy

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

Rotational Frequency given Velocity of Particle 1

Go Rotational Frequency = Velocity of Particle with Mass m1/(2*pi*Radius of Mass 1)

Rotational Frequency given Velocity of Particle 2

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

Angular Momentum given Moment of Inertia

Go Angular Momentum given Moment of Inertia = Moment of Inertia*Angular Velocity Spectroscopy

Angular Momentum given Kinetic Energy

Go Angular Momentum1 = sqrt(2*Moment of Inertia*Kinetic Energy)

Rotational Frequency given Angular Frequency

Go Rotational Frequency given Angular Frequency = Angular Velocity Spectroscopy/(2*pi)

Angular Velocity given Angular Momentum and Inertia

Go Angular Velocity given Momentum and Inertia = Angular Momentum/Moment of Inertia

Angular Velocity of Diatomic Molecule

Go Angular Velocity of Diatomic Molecule = 2*pi*Rotational Frequency

Angular Velocity given Inertia and Kinetic Energy Formula

Angular Velocity given Momentum and Inertia = sqrt(2*Kinetic Energy/Moment of Inertia)
ω2 = sqrt(2*KE/I)

How to get Angular velocity in terms of inertia and kinetic energy?

Rotational kinetic energy (K.E.) of a rotating object can be expressed as half of the product of the angular velocity of the object and moment of inertia around the axis of rotation (0.5*I* ω^2). So we get angular velocity as square root of twice of K.E. divided by moment of inertia (sqrt(2*K.E./I)).

How to Calculate Angular Velocity given Inertia and Kinetic Energy?

Angular Velocity given Inertia and Kinetic Energy calculator uses Angular Velocity given Momentum and Inertia = sqrt(2*Kinetic Energy/Moment of Inertia) to calculate the Angular Velocity given Momentum and Inertia, The Angular Velocity given Inertia and Kinetic Energy formula is a variation of K.E. formula. Kinetic energy of a rotating object can be expressed as half of the product of the angular velocity of the object and moment of inertia around the axis of rotation. So thus we get the relation between angular velocity, moment of inertia and K.E. Angular Velocity given Momentum and Inertia is denoted by ω2 symbol.

How to calculate Angular Velocity given Inertia and Kinetic Energy using this online calculator? To use this online calculator for Angular Velocity given Inertia and Kinetic Energy, enter Kinetic Energy (KE) & Moment of Inertia (I) and hit the calculate button. Here is how the Angular Velocity given Inertia and Kinetic Energy calculation can be explained with given input values -> 8.43274 = sqrt(2*40/1.125).

FAQ

What is Angular Velocity given Inertia and Kinetic Energy?

The Angular Velocity given Inertia and Kinetic Energy formula is a variation of K.E. formula. Kinetic energy of a rotating object can be expressed as half of the product of the angular velocity of the object and moment of inertia around the axis of rotation. So thus we get the relation between angular velocity, moment of inertia and K.E and is represented as ω2 = sqrt(2*KE/I) or Angular Velocity given Momentum and Inertia = sqrt(2*Kinetic Energy/Moment of Inertia). Kinetic Energy is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity & Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

How to calculate Angular Velocity given Inertia and Kinetic Energy?

The Angular Velocity given Inertia and Kinetic Energy formula is a variation of K.E. formula. Kinetic energy of a rotating object can be expressed as half of the product of the angular velocity of the object and moment of inertia around the axis of rotation. So thus we get the relation between angular velocity, moment of inertia and K.E is calculated using Angular Velocity given Momentum and Inertia = sqrt(2*Kinetic Energy/Moment of Inertia). To calculate Angular Velocity given Inertia and Kinetic Energy, you need Kinetic Energy (KE) & Moment of Inertia (I). With our tool, you need to enter the respective value for Kinetic Energy & Moment of Inertia 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 Angular Velocity given Momentum and Inertia?

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

Angular Velocity given Momentum and Inertia = Angular Momentum/Moment of Inertia
Angular Velocity given Momentum and Inertia = Angular Momentum/Moment of Inertia

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