Evidence from psychology, cognitive science, and neuroscience suggests that cognition and emotions are coupled. Education researchers have also documented correlations between emotions (such as joy, anxiety, fear, curiosity, boredom) and academic performance. Nonetheless, most research on students' reasoning and conceptual change within the learning sciences and physics and science education research has not attended to the role of learners' emotions in describing or modeling the fine timescale dynamics of their conceptual reasoning. The few studies that integrate emotions into models of learners' cognition have mostly done so at a coarse grain size. In this study, toward the long-term goal of incorporating emotions into models of in-the-moment cognitive dynamics, we present a case study of Judy, an undergraduate electrical engineering and physics major. We show that shifts in the intensity of a fine-grained aspect of Judy's emotions, her annoyance at conceptual homework problems, co-occur with shifts in her epistemological stance toward differentiating knowledge about and the practical utility of real circuits and idealized circuit models. We then argue for the plausibility of a cognitive model in which Judy's emotions and epistemological stances mutually affect each other. We end with discussions on how models of learners' cognition that incorporate their emotions are generative for instructional purposes and research on learning.