sometimes the universe Too complicated to analyze.
Heck, if you take a tennis ball and throw it across the room, even that is pretty complicated. After it leaves your hand, the ball has a gravitational interaction with the ground, causing it to accelerate toward the ground. The ball rotates as it moves, which means that there may be more frictional resistance on one side of the ball than on the other. The ball also collides with some oxygen and nitrogen molecules in the air – and some these Molecules eventually interact with it even more air. The air itself is not even stationary – the density changes as the ball moves higher, and the air can be in motion. (We usually call this wind.) Once the ball touches the ground, even the floor isn’t completely flat. Yes, it looks flat, but it is on the surface of a spherical planet.
But all is not lost. We can still model this tennis ball. All we need is some perfection. These are simplified approximations that turn an impossible problem into a solvable one.
In the case of a tennis ball, we can assume that all mass is concentrated in one point (in other words, that the ball has no actual dimensions) and that the only force acting on it is the constant gravitational force pulling downwards. Why is it okay to ignore all those other interactions? That’s because they don’t make a huge (or even measurable) difference.
Is this even legal in the court of physics? Well, the science is all about the model building process, including the equation of the trajectory of a tennis ball. At the end of the day, if the experimental observations (where the ball lands) agree with the model (predicting where it lands), we’re good to go. For the perfect tennis ball, everything works very we will. In fact, the physics of a thrown ball becomes a test question in an introductory physics class. Other idealization processes are more difficult, such as trying to determine the curvature of the Earth just by looking at this very long terminal at the Atlanta airport. But physicists do this kind of thing all the time.
Perhaps the most famous idealistic operation was performed by Galileo Galilei while studying the nature of motion. He was trying to figure out what would happen to a moving object if you didn’t exert a force on it. At that time, almost everyone followed the teachings of Aristotle, who said that if a force is not exerted on a moving object, it will stop and remain at rest. (Although his work was about 1,800 years old, people thought Aristotle was too great to be wrong.)
But Galileo did not agree. It was believed that it would continue to move at a constant speed.
If you want to study a moving object, you need to measure both position and time so that you can calculate its velocity or its change in position divided by the change in time. but there is a problem. How do you accurately measure the time that objects move at high speeds over short distances? If you drop something even from a relatively small height, such as 10 meters, it will take less than two seconds for it to reach the ground. Going back to about 1600, when Galileo was alive, that was a very difficult time period to measure. So, instead, Galileo looked at a ball rolling down the track.
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