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Idealized Models: An Introduction

Keep It Simple, Stupid

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I once heard an acronym for the best pieces of physics advice I ever got: Keep It Simple, Stupid (KISS). In physics, we are typically dealing with a system that is, in reality, very complex. For an example, let's consider one of the easiest physical systems to analyze . . .

Throwing a Tennis Ball

You throw a tennis ball into the air and it comes back, and you want to analyze its motion. How complex is this?

The ball isn't perfectly round, for one thing; it has that weird fuzzy stuff on it. How does that affect its motion? How windy is it? Did you put a little bit of spin on the ball when you threw it? Almost certainly. All of these things can have impact on the motion of the ball through the air.

And those are the obvious ones! As it goes up, its weight actually changes slightly, based on its distance from the center of the Earth. And the Earth is rotating, so perhaps that will have some bearing on the relative motion of the ball. If the Sun's out, then there's light hitting the ball, which may have energy repercussions. Both the Sun and the Moon have gravitational effects on the tennis ball, so should those be taken into account? What about Venus?

We quickly see this spiralling out of control. There's just too much going on in the world for me to figure out how all of it impacts on me throwing the tennis ball? What can we do?

Idealized Models in Physics

In physics, a model (or idealized model) is a simplified version of the physical system that strips away the unnecessary aspects of the situation.

One thing that we don't typically worry about is the physical size of the object, nor really its structure. In the tennis ball example, we treat it as a simple point object, and ignore the fuzziness. Unless it's something we're specifically interested in, we'll also ignore the fact that it's spinning. Air resistance is frequently ignored, as is wind. The gravity influences of the Sun, Moon, and other heavenly bodies are ignored, as is the impact of light on the surface of the ball.

Once all of these unnecessary distractions are stripped away, you can then begin focusing on the exact qualities of the situation that you're interested in examining. To analyze the motion of a tennis ball, that would typically be the displacements, velocities, and gravity forces involved.

Care with Idealized Models

The most important thing in working with an idealized model is to make sure that the things you're stripping away are things that are not necessary for your analysis.

If you're studying angular momentum, the spin of an object is essential; if you're studying 2-dimensional kinematics, it can be ignored. If you're throwing a tennis ball from an airplane at high altitude, you may want to take into account wind resistance, to see if the ball hits a terminal velocity and stops accelerating. Alternately, you may want to analyze the variability of gravity in such a situation, depending on the level of precision you need.

When creating an idealized model, make sure that the things you're eliminating are traits that you actually want to eliminate from your model. Carelessly ignoring an important element isn't a model, it's a mistake.

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