Noether's theorem, rotating potentials, and Jacobi's integral of motion

We consider the derivation of Jacobi's integral of motion for a particle moving in a uniformly rotating potential, as a simple illustrative application of Noether's theorem. We also provide some examples of Jacobi's integral. In particular, we show that some elementary problems usually discussed in texts of classical mechanics can be interpreted, in terms of Jacobi's integral. (C) 1998 American Association of Physics Teachers.