Our story starts in the cathedral of Pisa, in 1583, exactly. We are here with a medical student– a young, 19-year-old medical student with the name of Galileo Galilei You might know him. And precisely at that moment, an earthquake strikes in Tuscany. And Galileo notices that the chandeliers of the cathedral are swinging because of the motion of the Earth. But he notices that they are swinging with a period which does not depend on the weight of the chandeliers but depends on the length of the rope of each chandelier. So a very heavy chandelier is swinging the same period as a light one, as long as the length of the rope is the same.
And from this remark he will make a very far-reaching conclusion, which is that all objects are falling with the same motion in the gravitational field of the Earth.
Before returning to the study of Galileo of falling objects, let us pause for a moment in order to understand what was known at this time about the fall of material objects. All the ideas were coming from the Greeks, especially Aristotle, who identified three types of motion– the natural motion, like the motion when I drop this wood ball–
–a forced motion, which is a motion when I exert a force on this steel ball, for example–
–and a motion of a different kind– the circular motion of planets, stars, which was supposed to be a motion– a perfect motion– belonging to the skies, the harmony of the sphere. Since, as you probably know, Pythagoras was thinking that the distances between planets was according to musical intervals. Now Aristotle had studied the motion of objects. And he knew, as we can witness by letting a feather and a small steel ball fall, that they fall with different motion.
Clearly, the ball is heavier and falls more rapidly than the feather. He had experience, also, in different medium– for example, in a medium like water or in a medium like oil. And he was realising that the motion is different according to a medium, whether it’s air, water, or oil. And so he was concluding that the motion is necessary to a medium and concluding something which we’ll come back to, which is the fact that a vacuum is impossible, because in vacuum, motion would be impossible.
Galileo is believed to be the father of experimental physics. And in a second we’ll repeat one of his famous experiments– the inclined board experiment. He was also using heavily what are known as “thought experiments,” which are imagined experiments used in order to probe some hypothesis or to identify some concept. In modern days, theorists are making heavy use of these thought experiments. For example, when they study black holes– the horizon of a black hole, the environment of a black hole– they are making thought experiments in order to probe their understanding of gravity. And so we’ll make also some use of these thought experiments across this course.
Let me illustrate what a thought experiment is with a famous example due to Galileo himself, precisely about the fall of objects. So here I have two balls– two steel balls– a small one, a light one, and a heavy one. So let’s again test the fall of these two balls.
So you probably imagine, or your first intuition tells you, that this one is heavier so fell faster than the lighter one. And so Galileo tells you that if you believe so, then when you insert these two balls inside a bag, then this ball will be slowed down by the smaller ball. And so the two balls will fall slower than the larger ball. So let’s check that.
And so you see that your conclusion was that this bag of two balls is falling in a slower way than the individual ball– the larger ball. So that means that this bag of two balls, which is heavier, falls in a slower way than this unique ball. And so you see that you end up with a contradiction. So that shows, according to Galileo, that the hypothesis that you started with is not correct, and you have to revise your notions about the falling objects in the gravitational field of the earth.
And now a real experiment. Galileo had realised that when we drop balls, the motion is very fast, and it’s difficult to measure anything. Of course, you could go to Pisa tower. Supposedly he did so. But even there it takes time to measure the fall of different objects– objects of different composition. And so he proposed a different experiment, in order to slow down the motion, which is to use an inclined board like this one. So you can see immediately that you can study in more detail the motion of a ball.
And you can use different kinds of boards. You can use rough boards, you can use polished boards, you can use iced boards, in order to see also the effect of friction. Because, of course, there is more friction on a board than in the air. But you can change the friction by giving different surfaces to the board. And you can also compare the fall of two different objects– for example, this wood ball and this steel ball– by dropping them simultaneously.
And you see that they came to the bottom of the board at approximately the same time. They were falling with the same motion across the inclined board. So let us describe this experiment on the whiteboard.
So here is the inclined board where we dropped the ball. And the ball has been rolling down the ramp until it reaches the floor and then moves sideways. Now let us just imagine that we put another board inclined the opposite way at some distance. Then the ball will be rolling and be climbing up some distance. If there was no friction, then the ball would reach this position at the same height. But because there is friction, the ball will not reach the same height. But by making different experiments with different friction– a rough board, iced board, and so on– Galileo comes to the conclusion that if a board was without friction, then the ball would reach the same height.
Now, let me imagine that the slope of this ramp up is smaller. So it is less inclined. And, of course, in order to reach the same height, the ball will move to a longer distance.
And so the less inclined this board is, the further to the right the ball will be going, in the absence of friction. And so if we lower it completely and get back to the previous situation, Galileo concludes that– again, in the absence of friction– the ball will move forever, because it tends to reach the same height, but it cannot do it, because there is no ramping-up board. And so the ball will move forever. It has got what one calls “inertia.” So it’s a resistance to change of motion. It moves with constant velocity forever.
And so you see that, now, if we return to the example of a pendulum, which was the starting point of that story, then you see that this motion, here, it is not so different from the motion of a pendulum. Just imagine that this is a chandelier, and this is– there is a rope that attaches that chandelier. Then this motion, here, is somewhat similar to the motion that was identified in the cathedral of Pisa by Galileo. And you see that there are strong similarities between the situation that he was studying in the cathedral and the situation that we are studying here.
As we have just seen, by studying the fall of material objects Galileo identified a new principle, which he called the “principle of inertia,” that states that an object not subject to any external force will move at constant velocity in what one calls “uniform motion.”