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.

x-galileoPlace 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 \theta_{\textup{min}} (for minimum angle), and note that if you lower the plank below \theta_{\textup{min}}, the block stops.1 Now change the block, or IP, or both, and try to determine \theta_{\textup{min}} for the new set-up. The \theta_{\textup{min}} 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 \theta_{\textup{min}} 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.

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