Why the Weight of a Freely Falling Body Is Zero

The weight of a falling object disappears during the fall — proving this in the time of Galileo Galilei was no easy matter, and even today not everyone will believe that falling things weigh nothing at all. A body in free fall is one on which gravity is the only significant force acting, and under those conditions it registers no weight even though the gravitational pull on it never goes away.

The Weight of the Falling Body: What Galileo Discovered

Galileo Galilei discovered that a falling body loses its weight, meaning that during free fall an object exerts no force on a support and behaves as though weightless. This insight overturned the ancient belief, inherited from Aristotle, that weight is a fixed property clinging to every object. Weight, Galileo showed, is a force that appears only when something resists gravity — remove the resistance, let the object fall, and the weight vanishes for the duration of the fall.

This conclusion sits at the heart of modern physics and the way science shapes everyday life, from skydiving to spaceflight. It also foreshadows ideas later formalized by Isaac Newton in classical mechanics and, centuries afterward, by Albert Einstein in general relativity, where free fall is treated as the most natural state of motion of all.

Florence in the 16th Century and the Rise of Experimental Science

Florence in the 16th century, populated mainly by craftsmen, merchants and small manufacturers, was one of Italy's most developed cities, and it received Galileo warmly. Every artisan there understood plainly that skill was the product of personal labor and of the accumulated experience of many generations of craftsmen before him.

The Venetian glassmakers guarded and refined their secret recipes for centuries until they reached a perfection unmatched anywhere in the world. They achieved this not through abstract reasoning but through hard work and the countless experiments of their fathers, grandfathers and great-grandfathers. Their art was built by labor and experience.

Merchants of the age captained their own ships, endured storms, faced danger, took risks and wrestled with the elements, and they spoke with pride of a prosperity created by their own labor and experience. Armorers, dyers, tanners, jewelers and builders all knew that the road to mastery opened only through work and experience.

How the Bourgeoisie Valued Labor and Experience

When a scholar appeared who spoke the same plain, comprehensible language as the tradespeople, who was never at a loss for words in argument, who could work with his hands, knew the crafts, and trusted only experience, they accepted him as their own. Within the depths of the feudal order a new social class was growing and developing — the bourgeoisie, a word that in its original sense meant simply "town dwellers, city people."

The bourgeoisie of that time was revolutionary, and it was beginning a relentless struggle against feudalism. Galileo's insistence on evidence over authority made him a natural intellectual ally of this rising class.

Experiment as the True Method of Understanding Nature

Galileo did not become a servant of arrogant feudal lords. He rejected the mossy scholasticism of the feudal order, which refused to recognize anything beyond Aristotle. Galileo stood forth as the creator and defender of a new, bold science of nature — the science of townspeople, of the bourgeoisie — and held that the fundamental means of understanding nature is experiment.

Aristotle's Theory of Falling Bodies

Aristotle's theory of falling bodies held that heavier objects fall faster than lighter ones in direct proportion to their weight, and that weight is an intrinsic property every object always carries. For nearly two thousand years this claim was accepted on the authority of Aristotle alone, without systematic testing. The theory fails because it ignores the role of air resistance: in a vacuum, a feather and a lead ball fall at exactly the same rate, as later demonstrations would confirm.

Aristotle was not entirely unchallenged in the ancient and medieval world. John Philoponus, a 6th-century thinker, argued against the strict Aristotelian rule, and the Persian scholar Abu'l-Barakāt al-Baghdādī questioned the underlying dynamics. Historians of science such as Pierre Duhem later traced how these scattered objections prepared the ground for Galileo's decisive break with Aristotle.

Domingo de Soto's Early Contributions

Domingo de Soto, a 16th-century Spanish theologian and natural philosopher, was among the first to state clearly that a freely falling body accelerates uniformly — that it undergoes uniformly increasing motion — well before Galileo formalized the idea. His contribution shows that the concept of uniform acceleration in free fall did not spring from nowhere but emerged gradually across the historical development of physics.

This progression, running from Aristotle through medieval critics and de Soto to Galileo, Newton and Einstein, is a clear example of how scientific understanding is built cumulatively, each thinker correcting and extending the work of predecessors.

Galileo at the University of Padua

Galileo quickly found friends among the forward-looking people of his day. The Florentine Filippo Salviati and the Venetian Francesco Sagredo helped him secure a post. On their petition the Council of the Venetian Republic, by a majority of one hundred twenty-nine votes to three with nineteen abstentions — such was the popularity the young scholar had already earned — resolved to invite Galileo Galilei to the University of Padua as professor of mathematics and astronomy, granting him a salary three times what he had received at the University of Pisa.

Several years later Galileo's pay was doubled, then set at five hundred florins a year, and finally raised to a thousand florins — a sum never before paid to any mathematician in Italy. Galileo moved to the University of Padua in the autumn of 1592 and remained there for eighteen years.

Galileo's Most Important Discoveries

During his eighteen years at Padua, Galileo made his most important discoveries. He first repeated his student experiments with pendulums and continued his investigation of the free fall of bodies toward the earth. From this work grew the modern understanding of falling motion later systematized as Newtonian mechanics.

Experiments with Pendulums and Free Fall

A pendulum's swing, Galileo realized, is simply a modified form of falling. Pulling the bob to one side raises it away from the earth; releasing it lets it fall, but the string forces it to descend along a curved arc rather than straight down. Because the motion is a kind of fall, he could study the laws of falling by watching the steady rhythm of a swinging pendulum, which is far easier to time than a rapid drop.

Galileo took two balls of equal weight — one of lead, one of wood — hung them on threads of identical length, and set them swinging. He noticed that the wooden ball came to rest far sooner than the lead one: the lead was still swinging while the wooden ball already hung motionless. Something was draining the motion faster from the wooden ball, and Galileo identified the cause as air.

Air Resistance and Its Effect on Falling Bodies

Air resistance is the force that slows every moving object, and it explains why real falling bodies do not all descend at the same rate even though gravity accelerates them equally. Reflecting on a small failure during his experiment dropping two cannonballs at Pisa, Galileo concluded that air was to blame. The test had not taken place in a vacuum, so it was the air that forced the smaller ball to lag behind the larger one.

Air Resistance Definition and Mechanisms

Air resistance is the resistive push exerted by air on any object moving through it, and its presence can be seen and felt directly. When swinging balls sweep past the floor, specks of dust scatter — driven by the little breeze the balls stir up. Hold out a hand so the bob passes near the palm and you feel a faint puff of wind: the pendulum is shoving aside the air in its path.

Air slows the motion of all objects — falling, swinging, flying, large and small, light and heavy — but larger objects meet greater air resistance than small ones. A tuft of down always falls more slowly than a pebble; a woolen ball cannot be thrown as far as an iron weight. A grain of sand and a millstone ought to fall at the same speed, and if they do not, that is not a property of the objects themselves but the result of air resistance and the physical laws that govern motion.

A millstone is heavy and falls fast, but grind it into the finest dust and that dust will drift down for hours. Grinding does not change the total weight of the stone, yet it enormously increases the surface exposed to the air. The shape of a moving object matters greatly too, which is why streamlined bodies fall faster than flat or ragged ones of the same mass.

Aerodynamic Drag and Its Role

Aerodynamic drag is the specific form of air resistance that acts opposite to an object's direction of travel, and it grows stronger as the object moves faster. The drag force depends on the object's speed, its cross-sectional area, its shape as captured by a drag coefficient, and the density of the air. Because the drag force rises with velocity, a falling body cannot accelerate without limit — the faster it goes, the harder the air pushes back.

Galileo's observation that the larger wooden ball lost its motion faster is a direct consequence of drag depending on surface area. His insight that shape influences the fall anticipates the modern engineering practice of shaping projectiles, aircraft and skydivers' bodies to control drag.

Comparison Between Water and Air Resistance

Water resistance follows the same principle as air resistance but is far stronger, because water is roughly eight hundred times denser than air. An object dropped into water reaches a slow, steady descent almost at once, while the same object in air can accelerate for much longer before drag catches up. In both fluids the resisting force rises with speed and with the object's frontal area, so the physics is identical in kind and differs only in magnitude — a helpful way to picture why a dense medium tames motion so quickly.

Buoyancy, or upthrust, adds to the effect in both fluids: the surrounding medium pushes upward on a submerged or immersed object, reducing its apparent weight. Upthrust is much larger in water than in air, which is why a person floats in water but not in the atmosphere, though upthrust in air still matters for very light bodies such as balloons.

Free Fall in Classical Mechanics

Free fall in classical mechanics is motion in which gravity is the only force acting on a body, with no air resistance, buoyancy, or contact force present. Under these conditions every object, regardless of its mass, accelerates at the same rate toward the earth. Galileo's pendulum work led him straight to this principle, later placed on a rigorous footing by Isaac Newton and his laws of motion.

Definition and Principles of Falling Bodies

A body is in free fall when only gravitational pull acts on it. A dropped apple after it leaves the table, a skydiver before the parachute opens, and a spacecraft coasting in orbit are all — to a good approximation — in free fall. Objects that are not in free fall include a book resting on a shelf, a car on a road, or a parachutist under an open canopy, because in each case a contact force or air resistance opposes gravity.

Examples of what free fall is and is not:

• In free fall: a stone dropped from the Leaning Tower of Pisa in a vacuum, a coin released inside an evacuated tube, an astronaut orbiting the Earth.
• Not in free fall: a feather drifting down through air, a plane in level flight, an object sitting on a frictionless surface where the normal reaction force still balances gravity.

In a true vacuum, free fall follows simple equations of motion. Starting from rest, the velocity after a time t is v = g·t, and the distance fallen is s = ½·g·t², where g is the gravitational acceleration. With an initial velocity, these become v = v₀ + g·t and s = v₀·t + ½·g·t². These formulas underpin any free fall calculation used to solve physics problems, such as finding how far an object drops in a given time.

Comparison of Falling Objects with Different Masses

Two objects of different mass fall at the same rate in a vacuum, and Galileo's pendulum experiment demonstrated this decisively. He made two balls, one of lead and one of wood, arranging things so the lead ball was exactly one hundred times heavier than the wooden one. He tied them to threads of equal length, choosing that length so that each swing corresponded to two beats of his pulse, which made the swings easy to count.

Galileo drew both pendulums aside by the same distance and released them together. They swung in measured unison, like two soldiers marching in step: the heavy lead ball and the light wooden ball each completed fifty swings per hundred pulse beats. Over hundreds and thousands of swings he never once saw one pendulum gain even a hair on the other — the wooden ball kept pace with the lead ball though it was a hundred times lighter.

The weight of the balls plays no role here, and the reason is clear: the pendulum swings under the force of gravity, and its swing is only a disguised fall. In Galileo's own words:

By pulling the pendulum bob aside, I raise it, moving it away from the earth; when I release it, I give it freedom to fall, but it cannot fall straight down because the thread holds it. The bob is forced to descend along a curved line, along the arc of a circle. This motion of the bob is the same as falling, and so the weight of the balls has no effect on how often the pendulum swings.

The most striking real-world demonstration came in 1971, when astronaut David Scott dropped a hammer and a feather together on the Moon, where there is no air. Both struck the lunar surface at the same instant, confirming across three and a half centuries the very principle Galileo had inferred from his pendulums.

Gravitational Acceleration

Gravitational acceleration is the rate at which a freely falling body speeds up under gravity, and near the surface of the Earth it is about 9.8 metres per second squared. This means that with each passing second a falling object in a vacuum gains roughly 9.8 metres per second of speed, independent of its mass. The uniformity of this acceleration is exactly what Galileo's experiments revealed and what Newton's inverse-square law of gravitation later explained.

Gravitational acceleration varies from one celestial body to another because it depends on the mass and radius of the body. It is far weaker on the Moon and stronger on giant planets, so the same object would fall at different rates depending on where it is dropped:

• Earth: about 9.8 m/s²
• Moon: about 1.6 m/s², roughly one sixth of Earth's
• Jupiter: about 24.8 m/s²
• Sun: about 274 m/s²

Newton's law of universal gravitation describes the gravitational field as falling off with the inverse square of distance: double the distance from a body's centre and the pull drops to a quarter. This inverse-square law ties the fall of an apple to the orbit of the Moon, one of the great unifications in the history of physics.

Weight and Its Calculation (W = mg, F = ma)

Weight is the gravitational force acting on an object, calculated as W = m·g, where m is the mass and g is the gravitational acceleration, and it is measured in newtons. This follows from Newton's second law, F = m·a, since weight is simply the force that gravity supplies to accelerate a mass. A mass of one kilogram on Earth weighs about 9.8 newtons, whereas the same kilogram on the Moon weighs only about 1.6 newtons.

This makes clear why weight, unlike mass, changes across different celestial bodies: mass — the amount of matter — stays constant, but the gravitational pull that produces weight differs from Earth to Moon to Jupiter. Understanding this relationship shows why Aristotle was wrong to treat weight as a fixed, inseparable property of every object. Newton's third law adds a further layer: the earth pulls the object down, and the object pulls the earth up with an equal and opposite force, one of many real-life examples of action and reaction.

Loss of Weight in a Falling Body

Galileo's investigations did not stop with pendulums. By an ingenious line of reasoning he concluded that a falling object has no weight at all during its fall. Strange as it seems, water pouring from an upper bucket into a lower one loses weight while it is falling: an apple lying on a table has weight, but nudge it off the edge and for the time of its fall it loses that weight. This is genuinely true — the weight of a falling body disappears, and falling objects really do weigh nothing.

The Experiment with Falling Water

For a long time Galileo could not devise an experiment to measure the weight of a falling body and confirm that it weighs nothing, but many years later he succeeded.

At that moment the balance went out of equilibrium: the pan of weights outweighed the buckets and sank, while the buckets grew lighter and rose. The balance stayed in this position the whole time the water was flowing. But as soon as all the water had gathered in the lower bucket, the balance returned to equilibrium.

This instructive experiment shows that the portion of water in the stream — the part falling from the upper bucket to the lower — weighs nothing during its fall, and so the total weight of the water is reduced for as long as the stream is in the air.

The Experiment with a Falling Balance

Today this conclusion of Galileo's is proved very simply: hang a weight on the hook of a spring balance, then let the balance fall from your hand. In the first moments of the balance falling together with the weight, the pointer instantly jumps to zero — the weight no longer stretches the spring, because the falling body has lost its weight.

This means that weight is not something inherent in all objects, as Aristotle and other ancient Greek scholars maintained. Objects can lose their weight and go on existing perfectly well without it. What remains constant is the gravitational pull; what disappears is the force the object exerts on any support, which is what a scale actually measures.

Terminal Velocity

Terminal velocity is the constant maximum speed a falling object reaches when air resistance grows strong enough to balance the force of gravity. Up to that point the object accelerates, but the drag force increases with speed until it exactly cancels the weight, after which the net force is zero and the object stops speeding up. In a vacuum there is no terminal velocity, because there is no air to provide the balancing force — which is why free fall in a vacuum and falling through the atmosphere differ so sharply.

Definition and Explanation of Terminal Velocity

Terminal velocity is reached when the upward drag force equals the downward gravitational force on a falling body. A skydiver falling flat through the air reaches a terminal velocity of roughly 55 metres per second, or about 200 kilometres per hour, before opening a parachute. Opening the parachute suddenly increases the surface area, raising the drag force, so the skydiver decelerates to a much lower, safer terminal velocity for landing.

Why Acceleration Ceases at Terminal Velocity

Acceleration ceases at terminal velocity because the net force on the object becomes zero. While the object is slower than its terminal speed, gravity exceeds drag and the object accelerates; as speed rises, the drag force rises with it, shrinking the difference. Once drag equals gravity, there is no unbalanced force, so by Newton's first law the object continues at a steady speed rather than gaining any more.

Constant Velocity and Equilibrium States

At terminal velocity a falling object moves at constant velocity in a state of force equilibrium. This is a dynamic equilibrium: the object is still moving, and gravity is still pulling on it, but the forces cancel so there is no acceleration. Comparing weight at different stages makes the balance clear — before terminal velocity the object's apparent weight is reduced because it is accelerating and not fully supported; at terminal velocity the resisting air fully supports it, so a scale strapped to the object would register its full ordinary weight; and the true gravitational weight itself, the pull of the earth, never changes throughout the fall.

Weightlessness of Falling Objects

Any accelerated downward motion causes a person to lose their weight fully or partly, and this is the sensation of weightlessness. Weightlessness is not the absence of gravity but the absence of a supporting contact force — the gravitational pull is still there, yet the body feels no weight because nothing is pushing back against it. This is the crucial distinction between weightlessness and the disappearance of gravity: an astronaut orbiting the Earth is in continuous free fall, still gripped firmly by gravity, but feels weightless.

A partial loss of weight is pleasant and can even be enjoyable, which is why adults and children alike love swinging on a swing. When the swing goes down, the riders partly lose their weight and say their "heart skips" or their "breath is taken away." A person feels the same thing sledding or skiing down a steep slope, or riding the little cars of a roller coaster that plunges down each drop before climbing again.

The sensation of partial weight loss is familiar to people who live in tall buildings. Whenever they ride down in a fast lift, the cabin seems to drop away beneath their feet and the body becomes almost weightless — for a moment the falling body loses its weight. A full loss of weight is experienced by parachutists as they jump from a plane before the canopy opens, and by pilots who put an aircraft into a dive, sending it plunging rapidly toward the earth.

History records extraordinary examples of extended free fall. Joe Kittinger leapt from a balloon at the edge of space in 1960; Felix Baumgartner broke the sound barrier in free fall in 2012, jumping from about 39 kilometres; and Dr. Alan Eustace set a still higher record in 2014, falling from roughly 41 kilometres. Each of these jumpers experienced true free fall in the thin upper atmosphere before air resistance built up enough to slow them.

Circular Motion, Orbits, and Artificial Gravity

Orbital motion is a continuous free fall in which an object keeps missing the ground because it also moves sideways fast enough to follow the curve of the Earth. A satellite or spacecraft in orbit is falling toward the planet the whole time, yet its forward speed carries it around rather than down. This is why astronauts float: they and their spacecraft fall together at the same rate, so nothing presses them against a wall or floor.

Centripetal Force and Falling in Orbit

Centripetal force is the inward force that keeps an object moving in a circle, and in orbit that force is supplied entirely by gravity. Gravity plays the same role for an orbiting spacecraft that the string played for Galileo's pendulum bob — it bends the path into a curve instead of a straight line, exactly as Newton's laws require. A projectile thrown horizontally near the ground traces a parabolic trajectory, its horizontal and vertical motions independent; give it enough horizontal speed and the parabola widens into a closed orbit.

Spacecraft designers can also create artificial gravity by spinning a station so that the outward push of circular motion presses occupants against the outer wall, mimicking the pull of weight. This turns Galileo's insight inside out: where a falling object loses its weight, a rotating one can be made to feel weight where none would otherwise exist. Both effects flow from the same body of physics that runs from Galileo through Newton to Einstein, whose general relativity reinterprets free fall as motion along the natural, straightest path through curved space-time itself.

Conclusion: Galileo's Legacy in Understanding Falling Bodies

Galileo Galilei's central legacy is the demonstration that all objects fall at the same rate in the absence of air resistance and that a falling body loses its weight — conclusions reached through patient experiment rather than appeals to authority. In overturning Aristotle's theory of falling bodies, Galileo helped launch the experimental method that defines modern science, and his findings became the foundation on which Isaac Newton built classical mechanics and Albert Einstein built general relativity.

From the pendulums of Padua to the hammer and feather on the Moon, from skydivers reaching terminal velocity to astronauts floating weightlessly in orbit, the physics of falling bodies traces an unbroken line back to Galileo's insistence that nature is understood best through direct, honest experiment. That principle — trust the evidence — remains the beating heart of science today.