Center of Mass Calculation in Mechanics

This lecture covers the calculation of the center of mass for a homogeneous half-sphere using spherical coordinates, focusing on simplifying calculations by leveraging system symmetry. The instructor demonstrates the choice of appropriate coordinates and origin to simplify calculations, particularly for a system with axial symmetry. The lecture also delves into the concept of multiple integrals, emphasizing the importance of understanding the mechanics behind the center of mass calculation in various scenarios.