Motive force and centripetal force in Newton’s mechanics

Abstract

Newton’s concept of force was developed over a period of time, starting with a collisional model in his Waste Book, and culminating in his measure of the centripetal force at a point found in De Motu and again in Principia, Book I, Prop. VI. Newton kept developing his force concept, adding to it and making it many faceted. This rich concept of force has often posed difficulties for historians of science [for example, R. S. Westfall, Force in Newton’s Physics (MacDonald and American Elsevier, New York, 1971) and J. Herivel, The Background to Newton’s Principia (Oxford U.P., New York, 1965)] and others. These difficulties are related to at least six things as follows: (1) lack of understanding that Newton’s ‘‘motive force’’ is an abbreviation for ‘‘motive quantity of a force,’’ so that Newton’s ‘‘motive force’’ and his ‘‘force’’ are not two different types of force. Motive force (motive quantity) is used to quantify force; (2) lack of understanding of Newton’s model for instantaneous impulses; (3) lack of understanding that although Newton’s motive force has directionality Newton added it as a scalar in his analysis of uniform circular motion; (4) lack of understanding of Newton’s polygon model; (5) lack of understanding that Newton’s measure of the motive value of a force, the motive force, was always used to obtain a comparative measure of forces in his early mechanics; and (6) lack of understanding that Newton’s Prop. VI measure of centripetal force at a point permitted Newton to bring the time dimension into his motive force concept, thus developing it into something very close to our modern definition of force. This paper analyzes Newton’s development of his motive force concept, and discusses the difficulties that some scholars have had with various aspects of this concept.