AskPhysics

Because understanding the behavior of ideals is a building block to understanding the behavior of the complex environment.

Understanding f=ma is a lot easier when it's a non-relatavistic frictionless sphere in a vacuum, instead of trying to explain all of the tiny complicating factors all at once.

Once you know something is going to drop at 9.8m/s^2 without drag, you can start adding in drag equations and getting to more complex or more accurate answers, and that goes for many of that kind of thing

A few potential answers:

• Many times, ideal situations will be fairly close to the “real” answer, at least within an acceptable margin.
• You have to learn about the physics in the most basic sense before you can start adding on more complex physics and math. Many topics are just extensions of simpler problems with some added nuance.
• The more complex problems may require an understanding of the interactions at an atomic level, and it’s just not relevant to enough people to teach it in general classes.
• The math on more complex interactions often require more complex math than what you have learned at your given stage in school.
• The math on more complex interactions may also be “unsolvable” in the sense that you must use brute force iterative calculations to come to an acceptable margin of error.

In real life engineering, an approximation of a problem is often good enough to find a solution than needing to be totally accurate, as long as it is over-engineered to be within tolerance. For instance, if I need a shelf to hold 48.72 kg, I may as well round up to 50 kg and make the math easier.

Same with the gravitational constant or pi, why not just use 10, or 4? As long as you’ve rounded in the correct direction, and you’re within tolerance, you can make the calculations far easier by assuming away the unnecessary details. If force of drag from wind resistance is within my assumed tolerances, I can just not bother with the calculation, knowing that I have enough overhead.

It’s not the most optimal or cost efficient way of doing things, but it’s often faster and easier.

You have to walk before you run.

The maths are simpler, and you can adjust for whatever non ideal system you have

If you want to learn more on any subject, you need to start with the basics. Think of drawing, why do kids draw stick figures instead of photorealistic drawings of people? Gotta start somewhere and it’s easier, but still resembles reality enough for people to understand. If you want to make incredible art, you spend years honing your craft. If you want to do advanced math/physics, you spend years honing your craft.

"Assume a spherical cow..."

Because learning is something that happens through iteration and by combining new ans acquired knowledge together, it is sometimes simpler to learn some of these concepts by simplifying it to the essentials, which is good enough for a majority who will never go beyond that.

For example, the formula for the acceleration of gravity on Earth can be rounded to 9.8m/s². But that would be in an ideal situation, absent of air friction and other variables. But for most purpose and for learning, that is good enough.

A critical concept in physics and engineering is Superposition: the net (total) effect on a system is the sum of all component effects.

The "ideal" system is still there in any real physical system. It is not invalid in the slightest. The idealization is simply being modified by an infinite number of other smaller forces and interactions (friction, air resistance, earth rotation, etc) that cannot be easily quantified at your level. Once you learn the idealization, you can use superposition to add more components later on.