Rotational Energy of Non-Linear Molecule Calculator

✖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.ⓘ Moment of Inertia along Y-axis [I_y]			+10% -10%
✖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.ⓘ Angular Velocity along Y-axis [ω_y]			+10% -10%
✖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.ⓘ Moment of Inertia along Z-axis [I_z]			+10% -10%
✖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.ⓘ Angular Velocity along Z-axis [ω_z]			+10% -10%
✖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.ⓘ Moment of Inertia along X-axis [I_x]			+10% -10%
✖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.ⓘ Angular Velocity along X-axis [ω_x]			+10% -10%

✖Rotational Energy is energy of the rotational levels in the Rotational Spectroscopy of Diatomic Molecules.ⓘ Rotational Energy of Non-Linear Molecule [E_rot]

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Formula

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Rotational Energy of Non-Linear Molecule

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})

Example

34.57408 J = (0.5 \cdot 60 kg·m² \cdot {35 degree/s}^{2}) + (0.5 \cdot 65 kg·m² \cdot {40 degree/s}^{2}) + (0.5 \cdot 55 kg·m² \cdot {30 degree/s}^{2})

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Rotational Energy of Non-Linear Molecule Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
E_rot = (0.5*I_y*ω_y^2)+(0.5*I_z*ω_z^2)+(0.5*I_x*ω_x^2)
This formula uses 7 Variables

Variables Used

Rotational Energy - (Measured in Joule) - Rotational Energy is energy of the rotational levels in the Rotational Spectroscopy of Diatomic Molecules.
Moment of Inertia along Y-axis - (Measured in Kilogram Square Meter) - 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.
Angular Velocity along Y-axis - (Measured in Radian per Second) - 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.
Moment of Inertia along Z-axis - (Measured in Kilogram Square Meter) - 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.
Angular Velocity along Z-axis - (Measured in Radian per Second) - 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.
Moment of Inertia along X-axis - (Measured in Kilogram Square Meter) - 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.
Angular Velocity along X-axis - (Measured in Radian per Second) - 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.

STEP 1: Convert Input(s) to Base Unit

Moment of Inertia along Y-axis: 60 Kilogram Square Meter --> 60 Kilogram Square Meter No Conversion Required
Angular Velocity along Y-axis: 35 Degree per Second --> 0.610865238197901 Radian per Second (Check conversion here)
Moment of Inertia along Z-axis: 65 Kilogram Square Meter --> 65 Kilogram Square Meter No Conversion Required
Angular Velocity along Z-axis: 40 Degree per Second --> 0.698131700797601 Radian per Second (Check conversion here)
Moment of Inertia along X-axis: 55 Kilogram Square Meter --> 55 Kilogram Square Meter No Conversion Required
Angular Velocity along X-axis: 30 Degree per Second --> 0.5235987755982 Radian per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_rot = (0.5*I_y*ω_y^2)+(0.5*I_z*ω_z^2)+(0.5*I_x*ω_x^2) --> (0.5*60*0.610865238197901^2)+(0.5*65*0.698131700797601^2)+(0.5*55*0.5235987755982^2)

Evaluating ... ...

E_rot = 34.5740771457784

STEP 3: Convert Result to Output's Unit

34.5740771457784 Joule --> No Conversion Required

FINAL ANSWER

34.5740771457784 ≈ 34.57408 Joule <-- Rotational Energy

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Kinetic Theory of Gases » Equipartition Principle and Heat Capacity » Rotational Energy of Non-Linear Molecule

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< Equipartition Principle and Heat Capacity Calculators

Rotational Energy of Non-Linear Molecule

Go 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)

Translational Energy

Go Translational Energy = ((Momentum along X-axis^2)/(2*Mass))+((Momentum along Y-axis^2)/(2*Mass))+((Momentum along Z-axis^2)/(2*Mass))

Rotational Energy of Linear Molecule

Go 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))

Vibrational Energy Modeled as Harmonic Oscillator

Go Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2))

Rotational Energy of Non-Linear Molecule Formula

What is the statement of Equipartition Theorem?

The original concept of equipartition was that the total kinetic energy of a system is shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium. Equipartition also makes quantitative predictions for these energies. The key point is that the kinetic energy is quadratic in the velocity. The equipartition theorem shows that in thermal equilibrium, any degree of freedom (such as a component of the position or velocity of a particle) which appears only quadratically in the energy has an average energy of 1⁄2kBT and therefore contributes 1⁄2kB to the system's heat capacity.

How to Calculate Rotational Energy of Non-Linear Molecule?

Rotational Energy of Non-Linear Molecule calculator 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 calculate 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 calculate Rotational Energy of Non-Linear Molecule using this online calculator? To use this online calculator 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. Here is how the Rotational Energy of Non-Linear Molecule calculation can be explained with given input values -> 34.57408 = (0.5*60*0.610865238197901^2)+(0.5*65*0.698131700797601^2)+(0.5*55*0.5235987755982^2).

FAQ

What is Rotational Energy of Non-Linear Molecule?

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 and is represented as E_rot = (0.5*I_y*ω_y^2)+(0.5*I_z*ω_z^2)+(0.5*I_x*ω_x^2) or 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). 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, 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, 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, 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, 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 & 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.

How to calculate Rotational Energy of Non-Linear Molecule?

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 is calculated using 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 calculate Rotational Energy of Non-Linear Molecule, you need 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). With our tool, you need to enter the respective value for Moment of Inertia along Y-axis, Angular Velocity along Y-axis, Moment of Inertia along Z-axis, Angular Velocity along Z-axis, Moment of Inertia along X-axis & Angular Velocity along X-axis 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 Rotational Energy?

In this formula, Rotational Energy uses Moment of Inertia along Y-axis, Angular Velocity along Y-axis, Moment of Inertia along Z-axis, Angular Velocity along Z-axis, Moment of Inertia along X-axis & Angular Velocity along X-axis. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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