Authors: Ramzi Suleiman
Newton’s first law is expressed in textual form. It states that, unless acted upon by a net unbalanced force, an object will remain at rest, or move uniformly forward in a straight line. Accordingly, “inertial motion” means uniform rectilinear motion, while uniform circular motion is considered to be a noninertial, accelerated motion. This differentiation has resulted in the aftermath in different analytical treatments of the two types, both in classical and relativistic physics. In this short note, we show, based on Newton’s laws, that, contrary to the conventional differentiation between rectilinear and circular systems of motion, the two are dynamically equivalent, such that the set of laws describing the dynamics of one system correspond to an identical set of laws describing the dynamics of the second. An immediate corollary for the special case of uniform motion is that Newtonian physics is inconsistent with his first law and is, instead, consistent with Galileo’s definition of inertial motion. To rectify the apparent inconsistency, we propose a natural modification of the first law, which incorporates the case of uniform circular motion. By means of this inclusion, the first law can retain its unique standing, as a separate law that could not be deduced from the second law as a special case. We formulate the modified law textually and mathematically and comment briefly on the implication of the proposed modification to the theory and education of classical, and relativistic physics.
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