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50 PHYSICS 4.2 ARISTOTLE’S FALLACY true law of nature for forces and motion, one has The question posed above appears to be simple. to imagine a world in which uniform motion is possible with no frictional forces opposing. This However, it took ages to answer it. Indeed, the is what Galileo did. correct answer to this question given by Galileo in the seventeenth century was the foundation 4.3 THE LAW OF INERTIA of Newtonian mechanics, which signalled the birth of modern science. Galileo studied motion of objects on an inclined plane. Objects (i) moving down an inclined plane The Greek thinker, Aristotle (384 B.C– 322 accelerate, while those (ii) moving up retard. B.C.), held the view that if a body is moving, (iii) Motion on a horizontal plane is an interme- something external is required to keep it moving. According to this view, for example, an arrow diate situation. Galileo concluded that an object shot from a bow keeps flying since the air behind moving on a frictionless horizontal plane must neither have acceleration nor retardation, i.e. it the arrow keeps pushing it. The view was part of should move with constant velocity (Fig. 4.1(a)). an elaborate framework of ideas developed by Aristotle on the motion of bodies in the universe. Most of the Aristotelian ideas on motion are now known to be wrong and need not concern us. For our purpose here, the Aristotelian law of motion may be phrased thus: An external force is required to keep a body in motion. (i) (ii) (iii) Aristotelian law of motion is flawed, as we shall Fig. 4.1(a) see. However, it is a natural view that anyone Another experiment by Galileo leading to the sameconclusioninvolvesadoubleinclinedplane. would hold from common experience. Even a A ball released from rest on one of the planes rolls small child playing with a simple (non-electric) toy-car on a floor knows intuitively that it needs down and climbs up the other. If the planes are to constantly drag the string attached to the toy- smooth, the final height of the ball is nearly the car with some force to keep it going. If it releases same as the initial height (a little less but never greater). In the ideal situation, when friction is the string, it comes to rest. This experience is absent, the final height of the ball is the same common to most terrestrial motion. External as its initial height. forces seem to be needed to keep bodies in If the slope of the second plane is decreased motion. Left to themselves, all bodies eventually come to rest. and the experiment repeated, the ball will still reach the same height, but in doing so, it will What is the flaw in Aristotle’s argument? The travelalongerdistance. Inthelimitingcase,when answeris:amovingtoycarcomestorestbecause the slope of the second plane is zero (i.e. is a theexternalforceoffrictiononthecarbythefloor horizontal) the ball travels an infinite distance. opposesitsmotion.Tocounterthisforce,thechild In other words, its motion never ceases. This is, has to apply an external force on the car in the of course, an idealised situation (Fig. 4.1(b)). direction of motion. When the car is in uniform motion,thereisnonetexternalforceacting onit: theforcebythechildcancelstheforce(friction)by thefloor. Thecorollaryis:iftherewerenofriction, thechildwouldnotberequiredtoapplyanyforce tokeepthetoycarinuniformmotion. The opposing forces such as friction (solids) and viscous forces (for fluids) are always present in the natural world. This explains why forces by external agencies are necessary to overcome the frictional forces to keep bodies in uniform motion. Now we understand where Aristotle Fig. 4.1(b)The law of inertia was inferred by Galileo went wrong. He coded this practical experience from observations of motion of a ball on a in the form of a basic argument. To get at the doubleinclinedplane. Reprint 2026-27