Finding Torque by Eliminating Internal Forces

AbstractNewton's equations for individual particles contain many unknown internal forces, yet describing the overall motion of a body often does not require solving for each of them. Starting from a finite system of particles, this paper adopts three explicit assumptions: repulsive internal forces act only between prescribed neighboring particles, occur in equal and opposite pairs, and lie along the lines joining the interacting particles. Summing the particle equations first yields the equation of motion of the center of mass. The unused collinearity condition then suggests multiplying the component equations by transverse coordinates and subtracting, so that the internal forces again cancel in pairs. The remaining combination of external forces gives torque. Differentiation yields the angular momentum equation; imposing rigidity then yields the equation of planar rigid-body rotation. The treatment follows classical particle-system mechanics, emphasizing the origin of the coordinate weights, the role of each assumption, and the distinction between eliminating internal forces and checking whether a motion can be realized by repulsive forces. AI-assisted pre-publication checksChatGPT and Codex assisted with checking the mathematical derivations, references, and PDF layout before posting. These checks do not constitute Lean formal verification or peer review.