In most physics problems we usually ignore air resistance. That means we study and calculate the motion of objects as if air resistance isn't affecting anything - it doesn't exist. But what exactly is air resistance? Why do we usually ignore it?
The air around us on Earth (known as the atmosphere) might seem like empty space. But it actually consists of many different gases and particles. There are molecules of nitrogen, oxygen, carbon dioxide, water, and many other things "floating" all around us. When an object like a car or a ball is moving, it's constantly bumping into the molecules of air which apply a force back on the object as it moves. This force applied to a moving object from the air is what we call air resistance, or the drag force.
If you've ever stuck your hand out the window of a moving car, you've felt air resistance. We can almost think of air resistance as the resulting "wind" that a moving object feels, pushing back against its motion. In fact, the drag force is a type of frictional force. Instead of friction between the surfaces of two solid objects, drag is the friction between the surface of an object and the air around it.
Sometimes this interaction between an object and the air is very noticeable and the forces involved are significant. For example, a parachute experiences a lot of air resistance on purpose in order to slow down the person or object it's attached to.
So why do we usually ignore air resistance?
What is the equation for the force air resistance, also known as the drag force? We can see above that the drag force depends on 4 things (4 variables). Let's take a look at each one.
The first variable in the equation is air density. The denser the air, the larger the drag force. The air density is the mass of the air molecules in a given volume of space. So the more air molecules (and the more mass) that the object hits as it moves, the more air resistance the object experiences. The SI unit for density is kg/m³ (as a reference, typical air density near sea level is around 1.2 kg/m³).
The second variable in the equation is the drag coefficient of the object. The higher the drag coefficient, the larger the drag force. The drag coefficient is a number that usually falls between 0 and 2, and it depends on the shape, surface, and other characteristics of the object. A streamlined object with a smooth surface will have a lower drag coefficient and experience less air resistance, and a blunt object with a rough surface will have a higher drag coefficient and experience more air resistance. For example, an airplane wing may have a low drag coefficient of 0.05, and a train might have a higher drag coefficient of 1.8. Something to note is that the drag coefficient does not have a unit - we say that it's "unitless".
The third variable in the equation is the cross-sectional area of the object. The more cross-sectional area the object has, the higher the drag force. This cross-sectional area is the area presented in the direction of motion - it's the profile of the object that the air "sees" as the object moves. For example, the cross-sectional area of a ball (sphere) is a circle. With all of the other variables being held constant, more area means that the object hits more air molecules as it moves through the air, so it experiences more air resistance. The SI unit for area is m².
The fourth and possibly most important variable in the equation is the velocity or speed of the object (squared). The faster the object is moving, the more air resistance it experiences. This concept may be the one thing you're expected to know about air resistance. Notice that the velocity is squared, so if an object moves 3x as fast it will experience 9x the drag force.
So how does all of this factor in to the physics we're learning?
The motion of an object depends on the forces acting on it, and the drag force depends on the motion (velocity) of the object, so we get a complicated circle of cause and effect. In order to include air resistance in most problems and situations, we would need to use calculus. So for algebra-based lessons and physics problems, we ignore air resistance.
But what does it really mean to ignore air resistance? Well, the real-world version of ignoring air resistance is to study the motion of objects where there is no air to interact with. We call this a vacuum - which is why you might see something like "if we treat the object as a perfect sphere in a vacuum...". Imagine a giant tank or a room where we hooked up a strong vacuum pump and we sucked out all of the air molecules. This is what it's like in space, far away from Earth's atmosphere.
So how is the motion of an object different with and without air resistance?
The classic example is to imagine dropping a bowling ball and a feather at the same time from the same height. Normally, with air resistance, the bowling ball will land before the feather. The effect of air resistance on the feather's motion is more significant than the effect of air resistance on the bowling ball's motion, so the feather takes longer to hit the ground. However, if we did the same experiment in a vacuum with no air, the feather and bowling ball would land at the exact same time. Without air resistance, the only force that the objects experience is the force of gravity, which accelerates them both at the same rate (9.8 m/s²). This has actually been tested experimentally in a large vacuum chamber on earth, as well as by astronauts on the moon (where there is basically no air).
So the question is: when is it OK to ignore air resistance? The answer is: it depends. The amount of air resistance that an object feels depends on the four variables we mentioned above. And the impact it has on an object's motion also depends on a few other things. There is a continuous range of how much air resistance impacts the motion of an object, ranging from "it doesn't really matter" to "it matters a little" to "it matters a lot". But in general, one way we can think about it is like this:
If the force of air resistance (drag force) is similar in magnitude to the object's weight (gravitational force) like it is for a feather, then we should not ignore air resistance. Air resistance has a significant impact on the motion of that object, so if we ignore it we'll end up being very wrong when trying to predict its motion.
If the drag force is much smaller than the object's weight like it is for a bowling ball, then we might be able to ignore it. A smooth object with more mass tends to be more affected by other forces (like gravity) than by air resistance. So depending on how accurate we want to be about the object's motion, we might be able to ignore air resistance.
As an example, below is the trajectory of a cannonball with and without air resistance:
The black trajectory line is the real-world path of the cannonball with air resistance, and the yellow trajectory line is the path that our physics equations predict if we ignore air resistance. In this specific scenario, we can see that ignoring air resistance will still give us a pretty accurate prediction about the range of the cannonball. How accurate we want our predictions to be is up for us to decide based on the situation.
So to sum it up, all moving objects surrounded by air will experience a force of air resistance that pushes back against the motion. The amount of air resistance depends on several things, including the velocity of the object. Depending on the situation, air resistance may significantly affect an object's motion, or it might not. Whether or not we choose to ignore air resistance depends on how accurate we want to be for a given situation - how big of a difference is acceptable between our prediction when we ignore air resistance, and the actual motion?
In physics class, we usually want to study the motion of objects caused by other forces, ignoring air resistance. In the real world, it depends. If you're designing an electric scooter, you can probably ignore air resistance. If you're designing a plane, you better consider it.
In most physics problems we usually ignore air resistance. That means we study and calculate the motion of objects as if air resistance isn't affecting anything - it doesn't exist. But what exactly is air resistance? Why do we usually ignore it?
The air around us on Earth (known as the atmosphere) might seem like empty space. But it actually consists of many different gases and particles. There are molecules of nitrogen, oxygen, carbon dioxide, water, and many other things "floating" all around us. When an object like a car or a ball is moving, it's constantly bumping into the molecules of air which apply a force back on the object as it moves. This force applied to a moving object from the air is what we call air resistance, or the drag force.
If you've ever stuck your hand out the window of a moving car, you've felt air resistance. We can almost think of air resistance as the resulting "wind" that a moving object feels, pushing back against its motion. In fact, the drag force is a type of frictional force. Instead of friction between the surfaces of two solid objects, drag is the friction between the surface of an object and the air around it.
Sometimes this interaction between an object and the air is very noticeable and the forces involved are significant. For example, a parachute experiences a lot of air resistance on purpose in order to slow down the person or object it's attached to.
So why do we usually ignore air resistance?
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