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I understand that the average energy of each degree of freedom in a thermodynamic system in equilibrium is kT/2. My textbook says that for a monatomic gas particle, the only degrees of freedom that count are movement in three dimensional space, so the average energy of such a particle is 3kT/2.

My question is, why don't rotations contribute toward the average energy? My textbook suggests that this is because the moment of inertia is vanishingly small. However, my thought is that if the moment of inertia is very small, it just means that the particle would be spinning extremely fast in order to reach an average energy of kT/2 for each rotational axis.

sanbyakuman