Newton’s Second Law of a particle with variable mass

We approach the question of the movement of a particle with variable mass observed from an inertial frame. We consider two different situations: (i) a particle whose intrinsic mass value varies over time; (ii) the center of mass (CM) of a set of particles with constant mass but with a variable number of particles belonging to it. We show that Newton’s Second Law distinguishes the case in which the intrinsic mass of the particle varies over time from systems composed of particles, with constant mass, whose total mass varies over time. In the first case, we study the consequences of the equation of motion of a particle with variable mass is not covariant in inertial references under Galilean transformations. We also show that the equation that drives the dynamics of the CM of a system with variable number of particles preserves the equivalence of all inertial frames under the Galilean transformations. We verify the non-conservation of the linear momentum vector of the CM of a set of free particles during the time that one particle leaves or comes into the system.

Keywords
Mechanics; Newton’s Second Law; particle with variable mass; variable intrinsic mass of the particle; inertial frame; center of mass (CM) of systems with variable mass; linear momentum; mechanical energy