of an object have been worked out, we do not have to start all over again to find the center of mass of the whole object; we just have to put the pieces together treating each one as a point mass situated at the center of mass of that piece Let us see why that is. Suppose that we wanted to calculate the center of mass of a complete object, some of whose particles are considered to be members of object A and some members of object B. The total sum mix; can then be split into two pieces-the sum 2Amix: for the a object only, and the sum 2Bmixi for object B only. Now if we were computing the center of mass of object A alone, we would have exactly the first of these sums, and we know that this by itself is MAXA, the total mass of all the particles in A times the position of the center of of a, because that is the the of the center of m In the same manner, just by looking at object B, we get MBXB, and of course adding the two yields MX: MXO mx+∑mⅸ Now since M is evidently the sum of MA and MB, we see that Eq (19. 2)can be interpreted as a special example of the center of mass formula for two point objects, one of mass Ma located at Xa and the other of mass MB located at XB The theorem concerning the motion of the center of mass is very interesting and has played an important part in the development of our understanding of wton's law is right for the sm parts of a much larger object. Then this theorem shows that Newton, s law is also correct for the larger object, even if we do not study the details of the object, but only the total force acting on it and its mass. In other words, Newton s law has the peculiar property that if it is right on a certain small scale, then it will be right on a larger scale. If we do not consider a baseball as a tremend thing, made of myriads of interacting particles, but study only the motion of the center of mass and the external forces on the ball, we find F= ma, where F is the external force on the baseball, m is its mass and a is the acceleration of its center of mass. So F= ma is a law which reproduces itself on a larger scale.(There ought to be a good word, out of the Greek, perhaps, to describe a law which reproduces the same law on a larger scale Of course, one might suspect that the first laws that would be discovered by human beings would be those that would reproduce themselves on a larger scale Why? Because the actual scale of the fundamental gears and wheels of the universe are of atomic dimensions which are so much finer than our observations that we are nowhere near that scale in our ordinary observations. So the first things that we would discover must be true for objects of no special size relative to an atomic ale. If the laws for small particles did not reproduce themselves on a larger scale re would not discover those laws very easily. What about the reverse problem? Must the laws on a small scale be the same as those on a larger scale? Of course it is not necessarily so in nature, that at an atomic level the laws have to be the same as on a large scale. Suppose that the true laws of motion of atoms were given by some strange equation which does not have the property that when we go to a larger scale we reproduce the same law, but instead has the property that if we go to a larger approximate it by a certain expression such that, if extend that expression up and up, it keeps reproducing itself on a larger and larger scale. That is possible, and in fact that is the way it works. Newton,s laws are the tail end"of the atomic laws, extrapolated to a very large size. The actual laws of motion of particles on a fine scale are very peculiar, but if we take large numbers of them and compound them, they approximate, but only approximate, Newton's laws. Newton,'s laws then permit us to go on to a higher and higher scale, and it still seems to be the same law. In fact, it becomes more and more accurate as the scale gets larger and larger. This self-reproducing factor of Newton's laws is thus really not a fundamental feature of nature, but is an important historical feature. We would never discover the fundamental laws of the atomic particles at first observation because the first observations are much too crude. In fact. it turns