When we accelerate in a plane for takeoff, we feel ourselves pressed into the seat—this is Newton’s Second Law in practice. As linear momentum changes, we experience the opposite reaction. A similar sensation occurs just after landing, though in reverse—a sudden deceleration as the plane slows down.
Similarly, on a childhood swing, the same reaction plays out. At the highest point of its journey, just before changing direction, the swing momentarily pauses. Its velocity drops to zero, and just before that, we feel a jolt—the sensation of momentum fading.
The young woman in the picture above would no doubt come to understand the nature of changing momentum better than most. The forces she uncovered later in life were also found to carry momentum, just as objects do in everyday life—only on an atomic scale. Marie Skłodowska Curie and her work would be of momentous importance.
During her time and before, electrical pioneers spoke of electromagnetic induction as something akin to a change in momentum—with the so-called Lenz’s Law perceived as an action-reaction phenomenon. This is not a view that has lasted to the present day, an interesting topic in its own right.
Let’s start with what we can see and feel. Imagine a wooden chair that appears to be made of wood, yet is, in fact, constructed from an unexpectedly heavy material. Recall that sense of surprise—your mind anticipates lifting something of a certain weight, only to realize in the moment that it is much heavier. That instant, where expectation clashes with reality, is a direct encounter with mass, momentum, and inertia.
On the other side of the imaginable, a tightrope walker may carry a long but relatively light stick to maintain balance. We can all imagine the peculiar sensation of its “reluctance” to motion, offering stability—something that tangibly resists movement and yet has no appreciable weight.
And again, turning the problem around in our minds, we return to Newton, who spoke of “quantity of motion”—what we now call momentum. Experimentally, we may ask: Can weight alone be a reliable measure of “quantity“? Imagine a wooden-looking chair, deceptively made of lead, aboard a spaceship. In the absence of gravity, it would feel like nothing to lift. And yet, if you gave it momentum—a quantity of motion—you would definitely feel the force when it collided with your hand.
This tells us something important: mass alone does not determine an object’s effect—motion does. In Newton’s idea of quantity of motion, two elements come together: mass and speed. Their product—their multiplication—is what we now call momentum, and it was this very principle that Newton took as his starting point for understanding motion.
Now, let’s explore this idea in the context of rotation. When an object moves in a straight line, it carries linear momentum, but in a curve, things change. A centripetal force pulls the object inward to keep it on its circular path, while an opposing centrifugal tendency resists this, trying to push it outward.
This interplay between forces is strikingly evident when liquids of different densities are spun rapidly. If a tube holds two fluids liquids, that would not mix well—one heavier, one lighter—and is set into motion, the denser liquid shifts outward, while the lighter liquid remains nearer the axis. For a given speed, the heavier liquid possesses greater momentum (or quantity of motion), causing it to be flung further outward. A similar effect occurs with solid objects in liquid—a metallic ball moves outward, while a wooden ball, paradoxically, shifts inward, its lower mass resulting in a weaker outward force.
This reveals something fundamental about motion: momentum is not just about mass—it is about how mass interacts with force and motion itself. Just as a wooden chair that feels weightless in space can still hit hard if thrown, the denser liquid or heavier ball moves outward more forcefully in rotation, showing that momentum influences not only the impact of motion but also how objects rearrange themselves when movement is curved.
Whether it’s a swing slowing at its peak, the unexpected heaviness of an object when lifted, or the way substances behave in a spinning system, all of these phenomena trace back to the same principle. Motion is not just a property of objects—it is a relationship between mass, velocity, and force.
Having read a great many old physics books, I feel at liberty to introduce an older term into our musings–one that carries a certain elegance in language and may help us restore a way of speaking that once made ideas more accessible. In modern literature, inertia is often described as resistance to motion, but perhaps we could reclaim an older expression, one used by the brilliant yet often overlooked British mathematician Oliver Heaviside. Just as we intend—throughout this article and hopefully in a future book—to recover the clarity of older scientific language, we will use the term “reluctance” in place of resistance to motion, which fundamentally means inertia.
By doing so, we emphasize not just a passive property of mass, but an active unwillingness to accept changes in motion, a concept that resonates with both mechanical and electromagnetic principles. In this sense, reluctance (or inertia) and momentum stand on opposite sides of the equation, defining motion and its resistance in equal measure.
In this vein, we can reframe our earlier thoughts. Momentum describes how much motion an object carries, while reluctance (inertia) tells us how unwilling an object is to change its state of motion. These two ideas stand on opposite sides of an equation, balancing one another.
Think of momentum as the quality of motion, the property that allows movement to persist and be transferred. Think of momentum as the quality of motion, the property that allows movement to persist and be transferred. But if momentum is what carries motion forward, then reluctance, in the sense Oliver Lodge described, is the tendency to overshoot—to continue beyond the intended point, resisting any attempt to bring motion to a halt.
Lodge’s idea reframes inertia not as mere resistance to movement, but as an insistence on continuing, even when external forces try to restrain or redirect it. A moving body does not simply stop when a force ceases—it carries on, often beyond the expected limit, overshooting the target before finally settling into equilibrium. This is something we feel every day.
A train that comes to a stop still causes passengers to lean forward, their bodies overshooting the halt because their motion is not immediately canceled. A swing, rather than stopping at its highest point, momentarily defies gravity, stretching just beyond before reversing direction. Even in electrical circuits, current does not instantly cease when a switch is turned off—it lags, overshooting before stabilizing.
This brings us back to the duality of motion: momentum sustains movement, while reluctance resists change—but that resistance does not simply end motion, it causes it to push beyond, to linger, to overshoot. Lodge’s perspective reminds us that inertia is not just a passive property but an active persistence, a reluctance not just to start moving, but also to stop.
Reluctance (inertia), is therefore not so much motion itself but rather the unwillingness of an object to accept changes in motion–it expresses how much effort is needed to force a change. In a straight line, reluctance is tied to mass, but in rotation, it behaves differently. When something spins, its reluctance to change is shaped not just by how much mass it has, but where that mass is positioned in respect to the center of rotation. A wheel with its weight concentrated at the rim behaves very differently from one with its weight near the center–both in how easily it spins up and in how strongly it resists being stopped.
This balance between momentum and our reluctance (inertia) can be felt when making a sharp turn in a car or an airplane. You feel yourself pressed sideways, not because a force is throwing you outward, but because your body’s reluctance resists the change in direction. The vehicle turns, but your body wants to keep going straight, and only the seatbelt or the cabin wall provides the force to pull you into the new motion.
Now consider what happens inside an airplane as it comes to a stop. Small objects–a pen, a bottle–may slide forward along the floor. The plane slows down, but these objects, lacking friction to anchor them, keep moving. Heavier objects, on the other hand, show greater reluctance to sudden shifts in motion, making them harder to stop.
And so, the two sides of the equation emerge again: momentum sustains motion, while reluctance resists its change. This same principle governs the behavior of liquids with different densities when spun rapidly. If a tube holds two immiscible liquids–one heavier, one lighter–and is set into motion, the denser liquid shifts outward, while the lighter liquid remains closer to the axis. The heavier liquid carries more momentum but also exhibits greater reluctance–so when a force tries to alter its motion, it does not bend easily; instead, it moves outward. A similar effect occurs with solid objects in liquid–a metallic ball moves outward, while a wooden ball shifts inward, its lower mass giving it less reluctance to being moved.
Momentum is not just about motion–it is about how motion interacts with reluctance. Whether it’s a swing slowing at its peak, the unexpected weight of an object when lifted, or the way substances arrange themselves in a spinning system, all of these phenomena trace back to the same equation, where momentum and reluctance stand opposite one another, defining the nature of motion itself.
To give the reader a sense of the mathematical relationships at play without diving into formal equations, we can use simple proportional thinking and intuitive balance. Let’s construct a makeshift math–one that doesn’t rely on symbols but still lets us grasp the structure of these ideas.
1. The Balance Between Momentum and Reluctance
Let’s say you’re trying to push a heavy door open. The amount of effort you need depends on two things:
How heavy the door is (its reluctance to motion)
How fast you want it to start moving (its change in momentum)
A heavier door (more reluctance) requires a stronger push to get moving at the same speed as a lighter one. On the other hand, a faster push (more momentum) means you can make even a heavy door move more easily.
So we see a trade-off: if reluctance is high, you need more momentum to create the same effect. If reluctance is low, less momentum is needed to cause motion.
Now imagine this in a rotational sense–think of a merry-go-round at a playground. If all the kids sit near the center, it’s easy to start spinning it. But if they all move to the edge, suddenly, it feels much harder to get it turning. Why? Because reluctance in rotation depends on how mass is distributed.
If we imagine this as an equation without writing one, it might look like:
momentum change required = reluctance × how fast we change motion
This means if reluctance is doubled, it takes twice the effort (momentum change) to make the same shift in motion.
2. Why Objects Behave Differently in a Spinning System
Now, let’s revisit the spinning liquids example. Imagine we have two types of marbles–heavy metal ones and light wooden ones–inside a bowl, and we start spinning the bowl quickly.
The heavier marbles (more reluctance) don’t want to change their motion as easily, so instead of bending with the rotation, they push outward as if trying to maintain their straight-line motion.
The lighter marbles (less reluctance) follow along more easily, staying closer to the center.
So, if we think of outward motion in the spinning system, we can say:
How far an object moves outward is linked to its reluctance and how much motion it originally had.
This is why, in a washing machine, heavy clothes get pressed against the drum more forcefully than light ones–their greater reluctance makes them less flexible in following the circular motion, so they get flung outward.
3. How This Connects to Newton’s Third Law
Every time we push something, it pushes back on us with the same force–this is Newton’s Third Law.
If you push a wall, the wall pushes back, stopping you from going through it.
If you push a ball on ice, it moves away because nothing is pushing back as strongly.
Now think of the airplane braking example from earlier:
The heavy objects on the floor resist the stopping motion more because of their greater reluctance, so they don’t slow down as quickly.
The lighter objects get stopped more easily because they have less reluctance, so they slide more readily.
This also explains why inertia dampers in spacecraft or vehicles use heavy spinning wheels–their reluctance makes them resist changes in motion, helping stabilize movement.
4. The Big Picture: Momentum vs. Reluctance is the Backbone of Motion
So, in every case:
Momentum is what carries motion forward.
Reluctance is what resists changes in motion.
The greater the reluctance, the harder it is to change momentum.
The greater the momentum, the harder it is to stop or change direction.
This trade-off is what governs every motion we see, from a swing at the playground to the arrangement of substances in a rotating system, to even the motion of galaxies on a cosmic scale.
A Simple Thought Experiment for the Reader
To check if you truly understand these ideas, imagine this:
You are spinning in an office chair.
Your arms are stretched out wide.
Now, you pull your arms in.
What happens?
If you feel yourself speeding up, you’ve just experienced how reluctance in rotation works–pulling mass closer to the axis reduces reluctance, so your motion responds faster.
If you let your arms back out, you slow down because reluctance increases, demanding more effort to change speed.
That’s the invisible equation of motion at work–whether in a child’s game or the motion of planets.