Sliding and spinning behaviors significantly affect the performance of rolling bearings, especially for dry-lubricated bearings, micro and macro sliding may lead to increased wear of the solid lubricating film. A unified rolling contact tribology analytical model is proposed for dry-lubricated angular contact ball bearings (ACBBs) considering the extreme conditions including high combined loads and rolling contact effects. A comprehensive solution framework is proposed to ensure the robustness of the model under different loading conditions. Equilibrium equations are solved to study the effects of friction coefficients, rotating speeds, and combined loads on the skidding and spinning characteristics of the ACBB. The results show that the rolling contact effects and combined loads significantly affect the skidding and spinning performance of the ACBB. Further analysis reveals that the skidding mechanism is related to the interaction between ball kinematical motion and traction forces. The developed analytical model is proved to more accurately predict the bearing kinematical and tribological behavior as it discards the raceway control hypothesis and considers the macro/micro-slipping, creepage, and self-spinning motions of the ball, which is validated using both the existing pure axial loading dry-lubricated ACBB model and the classical Jones–Harris model. The study would provide some guidance for the structure and lubrication design of dry-lubricated ACBBs.