  We derive the one-dimensional optimal system for a system of three partial
differential equations which describe the two-dimensional rotating ideal gas
with polytropic parameter $\gamma >2.$ The Lie symmetries and the
one-dimensional optimal system are determined for the nonrotating and rotating
systems. We compare the results and we found that when there is no Coriolis
force the system admits eight Lie point symmetries, while the rotating system
admits seven Lie point symmetries. Consequently the two systems are not
algebraic equivalent as in the case of $\gamma =2~$ which was found by previous
studies. For the one-dimensional optimal system we determine all the Lie
invariants, while we demonstrate our results by reducing the system of partial
differential equations into a system of first-order ordinary differential
equations which can be solved by quadratures.
