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One of the objectives of the undergraduate physics curriculum is for students to become aware of the connections between the fundamental principles of classical physics and their personal experience. Nonetheless, numerous studies have shown that students' awareness of such connections tends to deteriorate, sometimes substantially, following instruction. In this work, which constitutes the first analysis of the effects of contemplative practices on the learning experience in undergraduate physics courses, we present two practices aimed at integrating formal theory with students' personal, embodied experience: a sensory meditation and a contemplative videography. In written reflections on their experiences with the practices, the students expressed suddenly becoming aware of countless manifestations of formal physics principles in their surroundings, in an important step toward establishing firm connections between the abstract and the experiential. Furthermore, the students reported experiencing a sense of physical embodiment, heightened sensory awareness, somatic relaxation, and mental stillness, in significant contrast to their typical experience. Students also described experiencing insight about the essential role of observation in the scientific endeavor, a reawakened sense of curiosity, an intrinsic motivation to understand the observed physical phenomena, and a deepened awareness of their cognitive and emotional processes.