Science education

How Galileo Discovered the Law of Inertia

The first law of motion is a very counter-intuitive beast! Every motion we encounter eventually ceases. Yet the first law states that motion persists forever (for objects that are isolated). The earliest version of the first law was stated by Galileo, who apparently came across it using his famous inclined planes.

Place a block of wood on a plank laid horizontally on the floor. When you raise one end of the plank, you create an inclined plane (IP). Keep raising the end of the plank until the block starts to move. Call this angle (for minimum angle), and note that if you lower the plank below , the block stops.1 Now change the block, or IP, or both, and try to determine  for the new set-up. The  will be different for different blocks and IPs. When the contact surface of the two is smoother, the angle will be smaller. Repeat the experiment for different levels of smoothness. These experiments will show you that

the smoother the surface of contact between the block and the inclined plane the smaller the minimum angle.

This statement is an example of induction, summarizing the results of several experiments in a brief statement – which could be mathematical – coming directly from observation. The statement is very much in tune with our common sense and intuition. And if Galileo had stopped here, he would have added nothing to our knowledge of motion.

Upon a stroke of genius, however, Galileo asked a deeper question: What  corresponds to an infinitely smooth surface of contact? Now, the concept of infinity is purely a mathematical concept; one that, analogous to the geometrical concept of a point, is not realizable in the physical universe. However, just as the concept of a point can be approximated by actual physical objects – such as the mark made by the tip of a sharpened pencil on a sheet of paper – so can the concept of an infinitely smooth surface be approximated by blocks and IPs that are more and more finely planed.

1. Actually, because the block is moving, you’ll have to lower the angle to a value that is smaller than the minimum angle for the block to stop. But this is just a technical detail.

Human mind is not fettered by the limitations of the instruments with which human hands occupy themselves. While the “hands” are extremely important in showing the direction in which human mind is to engage itself, it is the (trained) mind that takes us to the boundaries of knowledge and points us to the direction of nature’s hidden possibilities. This intervention of the human mind in the results of observation is called deduction. Deduction drags the secrets of nature out of their hiding places.

Although infinitely smooth surfaces do not exist in our immediate regions of contact with nature, their conceptual framework leads us to its hidden secrets. So, what if the surface of contact is infinitely smooth? What kind of  would we be getting? Since the minimum angle decreases with smoothness, we expect an infinitely small angle for an infinitely smooth surface. But what measure corresponds to an infinitely small angle? The answer is surprisingly obvious: zero! So, you need not raise an infinitely smooth surface to move the infinitely smooth block resting on it! “You need not raise” is too strong a statement. A better statement is to say “You need to raise the plank by a nonzero angle.” This angle could be a billionth of a trillionth of a quadrillionth of … a degree! A more meaningful way of stating the conclusion is to say that once in motion on a perfectly smooth horizontal surface, you cannot stop the block by manipulating the plank, because you can’t lower the angle below zero! In other words

On an infinitely smooth surface, an infinitely smooth block, once set in motion, will move on its own without any assistance from outside.

This is a restricted version of the first law of motion, or the law of inertia. It is in complete contrast with the Aristotelian law of motion whereby “any moving object must have a mover.” It is also in complete contrast with common sense. But what is common sense but, as Einstein said, a collection of “prejudices we accumulate by the age of eighteen.” And if the fundamental laws of physics were to have no dissonance with our common sense, they would be incapable of revealing to us the hidden secrets of the universe, which by their very nature escape our common sense.

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