Misguided Balloon
A floating balloon happens to accelerate in a direction that is seemingly misguided.
This article is focused on a physical phenomenon that seems very counterintuitive. Imagine we have a helium balloon that is being held by a string. We take it inside a car and tie the bottom of the string to the ground. The balloon floats straight up as it normally would. Figure 1 shows what this looks like. Now, if the car rounds a corner, what happens to the balloon? Does it stay straight up or tilt in some direction?
Before we talk about the balloon specifically, let's talk about centripetal and centrifugal forces to figure out what's going on here. When a car turns around a corner, it experiences a centripetal acceleration towards the "middle" of the turn. Newton's First Law of Motion defines inertia, which can be described as the resistance to acceleration. The force that we feel when we turn in a car (but is not an actual force as we are just experiencing inertia) is referred to as centrifugal force which is a fictitious force. However, the concept of forces is relative to a reference frame that we choose to observe motion from. For someone standing still on the ground and watching the car, they would understand forces how we conventionally describe them. For instance, there is a centripetal force pulling the whole car and its contents towards the curb when the car turns. Yet, a person inside the car is accelerating. This means that the reference frame that the person in the car experiences motion is also accelerating. In an accelerating reference frame, we use four principle fictitious forces (translational, centrifugal, Coriolis, and azimuthal) to account for motion, but for now, we only need the centrifugal force. For this article, let's consider a reference frame accelerating with the car. In this frame, the centrifugal force is what pushes you away from the curb when you turn a corner in a car.
Figure 1
Let's take a look at this car in Figure 2. It is taking a left turn, so naturally, the centrifugal force would be pointed towards the right (For the purpose of the article, let left signify the direction toward the inside of the turn and vice versa). The person driving the car would obviously slide to the right. Thus, most of us would naturally assume that the same would go for the balloon. In fact, it doesn't. We have overlooked that the balloon is filled with helium. I'll start with a complete, but personally unsatisfactory explanation. After that, we can look at exactly why the balloon behaves the way it does. In 1907, Albert Einstein introduced his equivalence principle (which led directly into general relativity, one of his two most famous discoveries) that stated the following: A gravitational force that an object feels is the same as a pseudo-force in a non-inertial reference frame. It just happens to be that centrifugal force on the balloon is a pseudo-force in a non-inertial reference frame. This means, for our purposes, the centrifugal force and gravity could be seen as equivalent, just in different directions. We already know that the balloon floats up in the air opposite to the direction of gravity, so if it is equivalent to the centrifugal force, it must float to the left away from the centrifugal force!
Figure 2
Let's look closer in the car and see what's happening to obtain a different explanation. The underlying idea here is that helium is less dense than the air around it on the Earth's surface. This means it will behave the same way an object floating in a liquid fluid does. The buoyant force pushes up on the balloon to make it float higher in the air (learn more about the buoyant force in the Disappearing Ice article). The buoyant force is supplied by pressure variations in the atmosphere as higher pressures near the bottom and lower pressures near the top of the balloon create a buoyant force greater than the gravitational force. When in the closed space of the turning car, the air inside the car also experiences the centrifugal force. It rushes into the space on the right (still referring to Figure 2) of the car which creates a pressure gradient once more. Higher pressure on the right side of the car and lower pressure on the left supply a buoyant force for the balloon to tilt left. To try and further the intuitive sense of the explanation, let's look at Figure 3. It shows a water bottle with an air bubble inside. As the bottle accelerates to the left, the fictitious force pushes the water to the right, leaving the air bubble on the left side. Our balloon situation is very similar, except we had "normal" air instead of water and a helium balloon instead of the air bubble. We are allowed to make this analogous comparison because the density of the air is less than that of water, similar to how the density of helium is less than that of "normal" air. Thus, we now have two very different and acceptable explanations for why a balloon will lean towards the inside of a turn.
Figure 3