The breakdown of the no-slip boundary condition at a fluid-solid interface has been recognized in micro/nanofluidics for many years. However, the relationship between the curvature of the surface and the degree of boundary slip has not been understood sufficiently well. The present study reveals that the degree of slip depends effectively on the surface curvature, which is having an opposing effect over rotating concave and convex surfaces. The results show that as surface curvature increases, the boundary slip becomes negligible over a concave surface, while it becomes increasingly important over a convex surface. In addition, boundary slip formulae are proposed that can accurately predict the boundary slips over convex and concave surfaces. These formulae are found to be in very good agreement with DSMC data for a range of accommodation coefficients and boundary curvatures. The present study then explains the mechanism of the intriguing phenomenon of velocity inversion which has, until the present study, often been mistakenly attributed solely to the effects of boundary curvature.