The rotation velocity asymmetry v observed in spiral galaxy HI rotation curves linearly correlates with the effective potential force from the 10 closest neighboring galaxies normalized for the test particle mass and the gravitational constant. The magnitude of the potential force from a close galaxy is proportional to the luminosity of the close galaxy and inversely proportional to the square of the distance from the close galaxy to the target galaxy. The correlation coefficient is 0.99 and F test is 0.99. Also, the slope of the rotation curve in the disk region of a galaxy from rising to flat to declining is qualitatively correlated with increasing asymmetry and, hence, to the net force from other galaxies. The result is based on a sample of nine spiral galaxies with published Cepheid distances and rotation curves and with a wide range of characteristics. These relationships are interesting not only for their predictive power but also because (1) they suggest a galaxy's dynamics and the shape of its rotation curve are related to the potential energy and distance of neighboring galaxies, (2) they suggest a rising rotation curve in the disk region is intrinsic, (3) they suggest the Tully-Fisher relationship's assumption that the mass to intrinsic luminosity ratio is constant among galaxies is valid, and (4) they are inconsistent with MOND, dark matter, and the Linear Potential Model.