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Rotational Energy of Non-Linear Molecule Formula

GoRotational Energy of Linear Molecule Formula

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Rotational Energy is energy of the rotational levels in the Rotational Spectroscopy of Diatomic Molecules. Check FAQs

E rot = (0.5 \cdot I y \cdot {ω y}^{2}) + (0.5 \cdot I z \cdot {ω z}^{2}) + (0.5 \cdot I x \cdot {ω x}^{2})

E_rot - Rotational Energy?I_y - Moment of Inertia along Y-axis?ω_y - Angular Velocity along Y-axis?I_z - Moment of Inertia along Z-axis?ω_z - Angular Velocity along Z-axis?I_x - Moment of Inertia along X-axis?ω_x - Angular Velocity along X-axis?

Rotational Energy of Non-Linear Molecule Example

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Here is how the Rotational Energy of Non-Linear Molecule equation looks like with Values.

Here is how the Rotational Energy of Non-Linear Molecule equation looks like with Units.

Here is how the Rotational Energy of Non-Linear Molecule equation looks like.

34.5741 = (0.5 \cdot 60 \cdot 35^{2}) + (0.5 \cdot 65 \cdot 40^{2}) + (0.5 \cdot 55 \cdot 30^{2})

34.5741J = (0.5 \cdot 60kg·m² \cdot {35degree/s}^{2}) + (0.5 \cdot 65kg·m² \cdot {40degree/s}^{2}) + (0.5 \cdot 55kg·m² \cdot {30degree/s}^{2})

34.5741 = (0.5 \cdot 60 \cdot 35^{2}) + (0.5 \cdot 65 \cdot 40^{2}) + (0.5 \cdot 55 \cdot 30^{2})

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Equipartition Principle and Heat Capacity » fx Rotational Energy of Non-Linear Molecule

Rotational Energy of Non-Linear Molecule Solution

Follow our step by step solution on how to calculate Rotational Energy of Non-Linear Molecule?

FIRST Step Consider the formula

E rot = (0.5 \cdot I y \cdot {ω y}^{2}) + (0.5 \cdot I z \cdot {ω z}^{2}) + (0.5 \cdot I x \cdot {ω x}^{2})

Next Step Substitute values of Variables

∴

E rot = (0.5 \cdot 60kg·m² \cdot {35degree/s}^{2}) + (0.5 \cdot 65kg·m² \cdot {40degree/s}^{2}) + (0.5 \cdot 55kg·m² \cdot {30degree/s}^{2})

Next Step Convert Units

∴

E rot = (0.5 \cdot 60kg·m² \cdot {0.6109rad/s}^{2}) + (0.5 \cdot 65kg·m² \cdot {0.6981rad/s}^{2}) + (0.5 \cdot 55kg·m² \cdot {0.5236rad/s}^{2})

Next Step Prepare to Evaluate

∴

E rot = (0.5 \cdot 60 \cdot {0.6109}^{2}) + (0.5 \cdot 65 \cdot {0.6981}^{2}) + (0.5 \cdot 55 \cdot {0.5236}^{2})

Next Step Evaluate

∴

E rot = 34.5740771457784J

LAST Step Rounding Answer

∴

E rot = 34.5741J

Rotational Energy of Non-Linear Molecule Formula Elements

Variables

Rotational Energy

Rotational Energy is energy of the rotational levels in the Rotational Spectroscopy of Diatomic Molecules.

Symbol: E_rot

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Rotational Energy

Moment of Inertia along Y-axis

The Moment of Inertia along Y-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Y-axis.

Symbol: I_y

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Moment of Inertia along Y-axis

Angular Velocity along Y-axis

The Angular Velocity along Y-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.

Symbol: ω_y

Measurement: Angular VelocityUnit: degree/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity along Y-axis

Moment of Inertia along Z-axis

The Moment of Inertia along Z-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Z-axis.

Symbol: I_z

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Moment of Inertia along Z-axis

Angular Velocity along Z-axis

The Angular Velocity along Z-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.

Symbol: ω_z

Measurement: Angular VelocityUnit: degree/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity along Z-axis

Moment of Inertia along X-axis

The Moment of Inertia along X-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about X-axis.

Symbol: I_x

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Moment of Inertia along X-axis

Angular Velocity along X-axis

The Angular Velocity along X-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.

Symbol: ω_x

Measurement: Angular VelocityUnit: degree/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity along X-axis

Other Formulas to find Rotational Energy

Go Rotational Energy of Linear Molecule

E rot = (0.5 \cdot I y \cdot ({ω y}^{2})) + (0.5 \cdot I z \cdot ({ω z}^{2}))

Other formulas in Equipartition Principle and Heat Capacity category

Go Translational Energy

E T = (\frac{{p x}^{2}}{2 \cdot Mass flight path}) + (\frac{{p y}^{2}}{2 \cdot Mass flight path}) + (\frac{{p z}^{2}}{2 \cdot Mass flight path})

Go Vibrational Energy Modeled as Harmonic Oscillator

E vf = (\frac{p^{2}}{2 \cdot Mass flight path}) + (0.5 \cdot K spring \cdot ({Δx}^{2}))

How to Evaluate Rotational Energy of Non-Linear Molecule?

Rotational Energy of Non-Linear Molecule evaluator uses Rotational Energy = (0.5*Moment of Inertia along Y-axis*Angular Velocity along Y-axis^2)+(0.5*Moment of Inertia along Z-axis*Angular Velocity along Z-axis^2)+(0.5*Moment of Inertia along X-axis*Angular Velocity along X-axis^2) to evaluate the Rotational Energy, The Rotational Energy of Non-Linear Molecule also known as angular kinetic energy is defined as the kinetic energy due to the rotation of an object and is part of its total kinetic energy. Rotational Energy is denoted by E_rot symbol.

How to evaluate Rotational Energy of Non-Linear Molecule using this online evaluator? To use this online evaluator for Rotational Energy of Non-Linear Molecule, enter Moment of Inertia along Y-axis (I_y), Angular Velocity along Y-axis (ω_y), Moment of Inertia along Z-axis (I_z), Angular Velocity along Z-axis (ω_z), Moment of Inertia along X-axis (I_x) & Angular Velocity along X-axis (ω_x) and hit the calculate button.

FAQs on Rotational Energy of Non-Linear Molecule

What is the formula to find Rotational Energy of Non-Linear Molecule?

The formula of Rotational Energy of Non-Linear Molecule is expressed as Rotational Energy = (0.5*Moment of Inertia along Y-axis*Angular Velocity along Y-axis^2)+(0.5*Moment of Inertia along Z-axis*Angular Velocity along Z-axis^2)+(0.5*Moment of Inertia along X-axis*Angular Velocity along X-axis^2). Here is an example- 34.57408 = (0.5*60*0.610865238197901^2)+(0.5*65*0.698131700797601^2)+(0.5*55*0.5235987755982^2).

How to calculate Rotational Energy of Non-Linear Molecule?

With Moment of Inertia along Y-axis (I_y), Angular Velocity along Y-axis (ω_y), Moment of Inertia along Z-axis (I_z), Angular Velocity along Z-axis (ω_z), Moment of Inertia along X-axis (I_x) & Angular Velocity along X-axis (ω_x) we can find Rotational Energy of Non-Linear Molecule using the formula - Rotational Energy = (0.5*Moment of Inertia along Y-axis*Angular Velocity along Y-axis^2)+(0.5*Moment of Inertia along Z-axis*Angular Velocity along Z-axis^2)+(0.5*Moment of Inertia along X-axis*Angular Velocity along X-axis^2).

What are the other ways to Calculate Rotational Energy?

Here are the different ways to Calculate Rotational Energy-

Rotational Energy=(0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2))

Can the Rotational Energy of Non-Linear Molecule be negative?

Yes, the Rotational Energy of Non-Linear Molecule, measured in Energy can be negative.

Which unit is used to measure Rotational Energy of Non-Linear Molecule?

Rotational Energy of Non-Linear Molecule is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Rotational Energy of Non-Linear Molecule can be measured.

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Rotational Energy of Non-Linear Molecule Formula

​GoRotational Energy of Linear Molecule Formula

Rotational Energy of Non-Linear Molecule Example

Rotational Energy of Non-Linear Molecule Solution

Rotational Energy of Non-Linear Molecule Formula Elements

Other Formulas to find Rotational Energy

Other formulas in Equipartition Principle and Heat Capacity category

How to Evaluate Rotational Energy of Non-Linear Molecule?

FAQs on Rotational Energy of Non-Linear Molecule

Variable Name

GoRotational Energy of Linear Molecule Formula