E = ½ I_{A}ω_{A}^{2} +½
I_{B}ω_{B}^{2}+ ½
I_{C}ω_{C}^{2}

with J_{i} = I_{i} ⋅ ω_{i} (J = angular
momentum) we obtain:

E = J_{A}^{2}/(2I_{A}) +
J_{B}^{2}/(2I_{B}) +
J_{C}^{2}/(2I_{C})

Some formulas to calculate moment of inertia are found here.
To begin, we assume the shape of the molecule to not be dependent on the
rotation, i.e. the length of bonds are*not* affected by centrifugal
forces. The molecule is thus regarded as *rigid* rotor in contrast to an elastic
rotor. We have to deal with the following cases

Spherical top | I_{A} = I_{B} = I_{C} = I |
e.g. CH _{4}, CCl_{4},
SF_{6} |

Symmetric top | I_{A} = I_{B} = I_{⊥} and I_{C} =
I_{||} I _{||}>I_{⊥} oblate
I _{||}<I_{⊥} prolate |
e.g. Benzene CH _{3}I |

Linear
rotor (a special case of symmetric top) |
I_{A} = 0, I_{B} = I_{C} |
all diatomic molecules, e.g. NO, C _{2}N_{2}, CO_{2} |

Asymmetric top | I_{A} ≠ I_{B} ≠ I_{C},
I_{A} ≠ I_{C} I _{A} < I_{B} <
I_{C} |
e.g. H _{2}O |

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