## 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)
Erot = (0.5*Iy*ωy^2)+(0.5*Iz*ωz^2)+(0.5*Ix*ωx^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
Erot = (0.5*Iyy^2)+(0.5*Izz^2)+(0.5*Ixx^2) --> (0.5*60*0.610865238197901^2)+(0.5*65*0.698131700797601^2)+(0.5*55*0.5235987755982^2)
Evaluating ... ...
Erot = 34.5740771457784
STEP 3: Convert Result to Output's Unit
34.5740771457784 Joule --> No Conversion Required
34.5740771457784 34.57408 Joule <-- Rotational Energy
(Calculation completed in 00.004 seconds)
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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

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)
Erot = (0.5*Iy*ωy^2)+(0.5*Iz*ωz^2)+(0.5*Ix*ωx^2)

## 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 Erot 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 (Iy), Angular Velocity along Y-axis y), Moment of Inertia along Z-axis (Iz), Angular Velocity along Z-axis z), Moment of Inertia along X-axis (Ix) & Angular Velocity along X-axis 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 Erot = (0.5*Iyy^2)+(0.5*Izz^2)+(0.5*Ixx^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 (Iy), Angular Velocity along Y-axis y), Moment of Inertia along Z-axis (Iz), Angular Velocity along Z-axis z), Moment of Inertia along X-axis (Ix) & Angular Velocity along X-axis 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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