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This lecture covers the mechanics of pulley systems and the establishment of equations of motion for coupled masses. Topics include the resolution of problems involving inclined planes with friction, kinetic friction, and the dynamics of pulleys. The lecture also delves into the analysis of sinusoidal regimes, transient behaviors, and the integration of instantaneous power to calculate energy losses. Additionally, it explores the concepts of rolling without sliding, center of mass calculations, and the dynamics of billiard shots.