Question

Classification of molecules on the basis of moment of inertia in physics

Answer 1

Classification of molecules on the basis of moment of inertia :
The principal axes are ordered such that associated inertia moments decrease, that is, the A-axis has the smallest moment of inertia and other axes are such that IA ≤IB ≤ IC. Depending on the relative size of the inertia moments, rotors can de divided into four classes.
Linear rotors
For a linear molecule IA << IB = IC. For most purposes IA can taken to be zero. For a linear molecule the separation of lines in the rotational spectrum can be related directly to the moment of inertia of the molecule. Since the moment of inertia is quadratic in the bond lengths, the microwave spectrum yields the bond lengths directly, provided the atomic masses are known.
Examples of linear molecules are obviously the diatomics such as oxygen (O=O), carbon monoxide (C≡O), and nitrogen (N≡N). But also many triatoms are linear: carbon dioxide(O=C=O), hydrogen cyanide (HC≡N), andcarbonyl sulfide (O=C=S). Examples of larger linear molecules are chloroethyne (HC≡CCl), and acetylene (HC≡CH).
Symmetric tops
A symmetric top is a rotor in which two moments of inertia are the same. Spectroscopists divide molecules into two classes of symmetric tops, oblate symmetric tops (frisbee or disc shaped) with IA = IB < ICand prolate symmetric tops (cigar shaped) with IA < IB = IC. Symmetric tops have a three-fold or higher rotational symmetry axis.
Examples of oblate symmetric tops are: benzene (C6H6), cyclobutadiene (C4H4), and ammonia (NH3). Prolate tops are: chloroform(CHCl3) and methylacetylene(CH3C≡CH).
Spherical tops
A spherical top molecule is a special case of a symmetric tops with equal moment of inertia about all three axes IA = IB = IC. The spherical top molecules have cubic symmetry.
Examples of spherical tops are: methane (CH4), phosphorus tetramer (P4), carbon tetrachloride(CCl4), ammonium ion (NH4+), and uranium hexafluoride (UF6).
Asymmetric tops
A rotor is an asymmetric top if all three moments of inertia are different. Most of the larger molecules are asymmetric tops. For such molecules a simple interpretation of the microwave spectrum usually is not possible. Sometimes asymmetric tops have rotational spectra that are similar to those of a linear molecule or a symmetric top, in which case the molecular structure must also be similar to that of a linear molecule or a symmetric top. In the determination of the molecular structure of asymmetric tops from microwave spectrum, isotopic substitution is invaluable.
Examples of asymmetric tops: anthracene(C14H10), water (H2O), and nitrogen dioxide(NO2).

Answer 2

Rotational inertia is important in almost all physics problems that involve mass in rotational motion. It is used to calculate angular momentum and allows us to explain (via conservation of angular momentum) how rotational motion changes when the distribution of mass changes.