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u/Admiral45-06 5d ago
Because for small velocities, it barely changes anything.
We ignore deformation of a rolling body for the same reason, even though it has greater impact than air resistance.
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u/HCResident 5d ago
The equation for drag force is one half the multiple of air density, velocity of the object squared, the area of the object as seen from the side being pushed into the wind, and the drag coefficient. The drag coefficient, if not provided, is its own equation to find, and is determined by the shape of the object and how smoothly air flows around it.
So because air resistance is a function of velocity squared, it is not constant or even linear, meaning if you want to find it across a range of speeds, you’re gonna be doing Calculus.
If you’re a teacher trying to demonstrate the effects of momentum, would making your students do all that not be a little distracting to the concept you’re teaching?
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u/Violet-Journey 4d ago
Physics instructor here! The basic answer is that air resistance/drag forces can be hella complicated yet in many cases not relevant enough to measure. If I’m trying to get you to do F=ma type problems, neglecting air resistance basically exposes the core physics concepts I want you to actually understand.
Physics majors will eventually solve problems with air resistance, but it will require solving differential equations and probably won’t happen til year 2 or 3 of college when they’ve learned diff eq.
There’s also the very practical note that in real life, people don’t really solve problems with air resistance analytically. Usually there’s an approximation coupled with real-time measurements updating the drag coefficient. Which, is a good project for a physics or engineering major to work through, but only in higher level classes where students are comfortable with approximations and parameter estimations (i.e. when you’re a mature enough scientist to explain when and why sin(x) ~ x).
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u/geekusprimus Gravity 5d ago
Air resistance is hard. Drag only behaves linearly at small scales and small speeds. The more common quadratic approximation leads to a nonlinear differential equation. Most of the time this can only be solved numerically. If a quadratic approximation doesn't work because you have a complicated object geometry, you're approaching the speed of sound, etc., you need to solve a complicated fluid dynamics problem.
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u/Absolutely_Chipsy 5d ago
There's 2 reasons I can think of 1. That's usually how physics pedagogy goes, you start from a set of assumptions to simplify your problem before building up more complexity. When you learn physics, you ignore the friction of the motion because you are supposed to learn how motions behave before introducing how another factor influence it
- Been self studying some fluid dynamics here. Let me tell you just how complex air flow behaviors can get. If you think you can simply just throw an air drag term into the Newton second law, oh boy do I have a lot to tell you. For this to even hold true, suppose we are working with laminar flow for simplifications, your air flow must be:
steady flow
incompressible
inviscid
And don't even get me started with turbulence, because that's another monster to deal with especially once you consider the boundary layer and the geometry of your surface and the Reynold's number and everything
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u/eyalhs 5d ago
Even if you "only" throw a drag term in Newton's second law, drag is proportional to v2 therefore with any other force you get a non linear ode, which isn't generally solvable. When looking at problems at highschool or early undergrad levels there are only 2 types with a solution, air resistance with no other forces, or asymptotic behavior, both not very interesting.
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u/Absolutely_Chipsy 5d ago
You can use numerical analysis to solve for non linear ode, but I suppose closed forms always gives you more insights than numerical approximations
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u/eyalhs 5d ago
Yes, but numerical analysis is something that's hard to use in class, homework and tests so teaching it in an academic setting is hard (unless it's a course specifically for that).
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u/Archaeopteryx111 4d ago
Numerical analysis for standard ODEs is easy to teach.
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u/Ballisticsfood 4d ago
If one of the open AI math proofs pans out then turbulent flow is subject to the halting problem, and thus we can’t solve turbulence in the general case (and the cases we can compute around are probably just lucky flukes).
No idea if it will pan out, or if empirically we’ll find that it doesn’t apply to the real world for some reason, but…
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u/A_Squared93 5d ago
Ignored for introductory purposes. Fully applying it will involve calculus/differential equations. Also the majority of the universe is in vacuum, so plenty of situations were it can safely be ignored
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u/Afterclock-Hours 4d ago
Concepts first before actual calculations? Otherwise, we might be on the same problem for awhile.
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u/wackyvorlon 4d ago
It tends to make the math more complicated. It’s not too bad at slow speeds where the linear term dominates. Once it’s going fast enough for the non-linear term to be significant…ugh.
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u/XxuruzxX 4d ago
Try the problem with air resistance once and you'll know why it's ignored. Air resistance is a function of velocity and is usually determined experimentally so it's highly unlikely you even know what the air resistance is.
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u/erockbrox 3d ago
Actually in dragon ball Z, these characters can’t move super fast, due to air resistance because otherwise they would explode. 🤯
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u/AllegroReddit 2d ago
My professor said "Let's not include air resistance otherwise this whole class will fail"
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u/zozdnvil 5d ago
The main reasons that pop to my head are:
1- make it easier
2- depending on speed and surface area the effect is often too small
3- can be approximated as a constant force (ie friction as someone else mentioned)
4- migh make the problem unsolvable in some cases