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We derive the one-dimensional optimal system for a system of three partialdifferential equations which describe the two-dimensional rotating ideal gaswith polytropic parameter $\gamma >2.$ The Lie symmetries and theone-dimensional optimal system are determined for the nonrotating and rotatingsystems. We compare the results and we found that when there is no Coriolisforce the system admits eight Lie point symmetries, while the rotating systemadmits seven Lie point symmetries. Consequently the two systems are notalgebraic equivalent as in the case of $\gamma =2~$ which was found by previousstudies. For the one-dimensional optimal system we determine all the Lieinvariants, while we demonstrate our results by reducing the system of partialdifferential equations into a system of first-order ordinary differentialequations which can be solved by quadratures.

One-dimensional optimal system for 2D Rotating Ideal Gas