# Rotation

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The rotation of macroscopic body around fixed axis is given by E = ½ Iw2 where w is the angular velocity [radian · s-1] and I = mr2 is the inertia moment of mass m on the distance r from the fixed axis. (It can be compared with kinetic energy E = ½ mv2; I comes from m and w comes from v). A body that can freely rotate around three axes (A, B, C) which are also referred to as the main inertia axes has a rotational energy (classically):

E = ½ IAwA2 + ½ IBwB2 + ½ ICwC2

with Ji = Ii · wi (J = kinetic moment) we obtain the following:

E = JA2/(2IA) + JB2/(2IB) + JC2/(2IC)

One can find few formulas for Calculation of inertia moments here. Now we don't consider the strainless molecules. We talk about stationary top or stationary rotator contrary to the moving rotator. We differ the following four cases:

- Spherical top: | IA = IB = IC = I | CH4, CCl4, SF6
- Symmetric top: | IA = IB = I^ and IC = I|| I||> I^ oblate I||< I^ prolate | Benzene CH3I
- Linear top: | IA = 0, IB = IC (all diatomic molecules) | NO, C2N2, CO2
- Asymmetric top: | IA ¹ IB ¹ IC, IA ¹ IC IA < IB < IC | H2O