The center of mass (CM) in a 3D coordinate system can be calculated using specific formulas depending on the distribution of mass. For a system of particles, the CM is determined by the formula [Σ mi * ri] / total mass, where mi is the mass of each particle and ri is its position vector. In the case of a continuous mass distribution, the CM is found using the triple integral [∫ r * ρ(r) dV] / total mass, where ρ(r) represents the density at position r. The position vector r is defined in Cartesian coordinates as r = xi + yj + zk.
PREREQUISITESStudents in physics or engineering, mathematicians focusing on calculus, and professionals involved in mechanical design or structural analysis will benefit from this discussion.