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This lecture covers the concept of the center of mass, also known as the center of gravity or center of inertia, which is crucial for systems of material points and solids. The instructor explains the definition of the center of mass, its operational significance, and its independence from the choice of origin. The lecture delves into the properties of the center of mass, its usefulness in simplifying the laws of motion, and its role in analyzing systems of material points and solids. The discussion extends to the concept of reduced mass and its application in solving two-body problems, emphasizing the importance of considering the center of mass and relative positions in such scenarios.