An accurate theoretical formula for linear momentum, force and kinetic energy

Abstract

The paper demonstrates that the existing mathematical formulas of linear momentum, force and kinetic energy in physics are incomplete, since such formulas have been formulated without incorporation of mass-energy equivalence relation E = mc². Therefore, new reformulations of the main equations of linear momentum, force and kinetic energy in the realm of special relativity are proposed. The proposed formulas provide same mathematical outcomes as the old formulas, displaying same behavior of the system when velocity approaches to speed of light, but, most importantly, comprise only velocity of the light and mass of object to provide well-defined expressions. [Formulae available with the full text]. These formulas vividly reveal that every physical variable depends solely on relativistic mass. Therefore, it modifies Newton’s second law of motion and states that the force depends on rate of change of relativistic mass of object rather than its velocity. In this highly interesting topic, primary purpose here has been to present a succinct and the carefully reasoned account of a new aspect of the Newton’s second law of motion which properly allows to derive the new mathematical formulas of linear momentum, force and kinetic energy.