Based on the magnitudes of their moment of inertia, molecules can be categorized. Moment of inertia is a unit of measurement for a molecule’s resistance to rotational motion around a specific axis. It is based on how the molecule’s mass is structured.

__FORMULA FOR MOMENT OF INERTIA__

- I = Σmr²,

where m denote the mass of each particle in the molecule, and r gives information about the distance of each particle from its rotational axis , can be used to calculate the moment of inertia of a molecule.

__On basis of moment of inertia values the molecules can be classified into following three types:__

__LINEAR MOLECULES :__

The moment of inertia of linear molecules is higher around the axis perpendicular to the molecular axis and smaller about the latter. This is so that the molecule can freely rotate about its molecular axis, where the mass is dispersed. The molecules CO2, HCN, and OCS are examples of linear molecules.

__NON LINEAR MOLECULE:__

Non-linear molecules have an increased moment of inertia around their molecular axis compared to their perpendicular axes. Molecular axis cannot be freely rotated because the mass is centered away from it. The examples of non-linear molecules includes:

- methane (CH4)
- ammonia (NH3)
- and water (H2O) etc.

__SPHERICAL MOLECULE__

The moment of inertia for spherical molecules is the same along all axes due to equal distribution of mass around the moleculer axis. The examples of spherical molecules are given below:

- Carbon dioxide (CO2).
- sulphur dioxide (SO2).
- and carbon disulfide (CS2).

__NOTE:__

In the study of molecular spectroscopy, the classification of molecules based on their moment of inertia is very difficult because it enables us to explain the structure of the molecule and the characteristics of its vibrational and rotational modes.