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Abstract
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.
Highlights
The three laws stated by Sir Isaac Newton in his “Philosophiae Naturalis Principia Mathematica” in 1687 [1] describe the movement of the classical particles and extended bodies
We have two aims: (i) to study the consequences of Newton’s Second Law in describing the motion of a particle whose intrinsic mass varies over time; (ii) to verify if the equation derived in reference [9] for the movement of a center of mass (CM) of a set of particles of constant mass and whose number of components varies over time of one unit is covariant in all inertial frames under the Galilean transformations
In Physics textbooks, the Newton’s Second Law that describes the motion of particles followed by observers at rest in inertial frames, relates the time variation of their linear momentum vectors with the vector resulting from the physical forces acting on them
Summary
The three laws stated by Sir Isaac Newton in his “Philosophiae Naturalis Principia Mathematica” in 1687 [1] describe the movement of the classical particles and extended bodies. We have two aims: (i) to study the consequences of Newton’s Second Law in describing the motion of a particle whose intrinsic mass varies over time; (ii) to verify if the equation derived in reference [9] for the movement of a CM of a set of particles of constant mass and whose number of components varies over time of one unit is covariant in all inertial frames under the Galilean transformations. The discussion of these two items will allow us to answer the question previously presented. In Appendix A we present the solutions of Newton’s Second Law in a particular inertial frame for some special forces
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