Drop a stone and a crumpled sheet of paper at the same time and the stone wins. Drop the same stone and the same paper inside a vacuum chamber and they land together. Gravity did not change between the two experiments — the air did. That difference is the whole story behind terminal velocity, one of the most useful ideas in introductory physics.
Free fall in an ideal world
In physics problems where air is ignored, a falling object accelerates at a constant rate near the Earth’s surface, usually written as g and taken as roughly 9.8 metres per second squared. Every second, the object gains about 9.8 m/s of downward speed, and it never stops gaining.
Crucially, this acceleration does not depend on mass. A heavy ball and a light ball dropped in a vacuum accelerate identically, because the larger gravitational force on the heavier object is exactly offset by its greater inertia. This is the result famously demonstrated on the Moon, where a hammer and a feather were dropped together and hit the surface at the same moment.
On Earth, though, we are at the bottom of an ocean of air — and air pushes back.
Air resistance: a force that grows with speed
As an object moves through air, it has to shove air molecules out of the way. Those molecules push back, producing a drag force that opposes the motion. The key property of drag is that it is not constant: the faster you go, the stronger it gets.
For everyday objects falling through air, drag depends on several things:
- Speed — the dominant factor. At the speeds typical of falling objects, drag rises roughly with the square of the velocity, so doubling the speed produces far more than double the drag.
- Cross-sectional area — a flat sheet presents far more area than the same sheet crumpled into a ball.
- Shape — a streamlined form lets air flow around it more smoothly than a blunt one.
- Air density — thinner air at high altitude produces less drag than dense air at sea level.
How terminal velocity emerges
Now follow a falling object from the moment it is released.
- At rest, speed is zero, so drag is zero. Only gravity acts, and the object accelerates at its maximum rate.
- As speed builds, drag appears and grows. The net downward force — weight minus drag — shrinks.
- With less net force, acceleration decreases. The object still speeds up, but more gently each second.
- Eventually drag grows until it exactly equals weight. Net force becomes zero.
- With no net force, acceleration is zero. The speed stops changing. That steady speed is terminal velocity.
Notice what terminal velocity is not. The object is not slowing down, and it is not weightless. Gravity is pulling just as hard as before; drag is simply cancelling it. This is a direct illustration of Newton’s first law: balanced forces produce constant velocity, not rest.
Why mass matters here but not in a vacuum
This is the part that trips students up. In a vacuum, mass cancels out and everything falls the same. With air, mass matters again — but indirectly.
Drag depends on size and shape, not on mass. A heavier object of the same size and shape has more weight to be cancelled, so it must reach a higher speed before drag can match it. That is why a solid steel ball falls faster than a hollow plastic ball of identical diameter, and why crumpling a sheet of paper makes it fall faster: crumpling does not change its mass, but it slashes the area that produces drag.
| Change | Effect on drag | Effect on terminal velocity |
|---|---|---|
| More mass, same shape | Unchanged | Higher |
| Larger cross-sectional area | Greater | Lower |
| More streamlined shape | Smaller | Higher |
| Thinner air (high altitude) | Smaller | Higher |
Everyday examples
Once you know what to look for, terminal velocity shows up everywhere.
- Raindrops. Falling from clouds thousands of metres up, raindrops would arrive at devastating speeds without air. Instead they reach a modest terminal velocity within the first fraction of their fall, which is why rain is survivable.
- Parachutes. A parachute does not fight gravity; it multiplies drag by dramatically increasing area. The skydiver’s terminal velocity drops to a value soft enough for landing.
- Dust and pollen. Very small particles have tiny terminal velocities, so they hang in the air for a long time and drift with the slightest breeze.
- Skydivers changing position. Spreading arms and legs increases area and slows the fall; tucking into a streamlined dive increases speed. Nothing about the skydiver’s mass changes.
A note on scale
Small animals often survive falls that would injure larger ones, and terminal velocity is part of the explanation. As an object shrinks, its surface area decreases more slowly than its volume and mass. That gives small creatures a relatively large drag force compared with their weight, and therefore a much lower terminal velocity.
The same geometric relationship explains why fine powders float in the air while a solid lump of the same material drops straight down.
Common misconceptions
- “Heavier things always fall faster.” Only when air resistance is involved, and only because greater weight needs more drag to balance it.
- “At terminal velocity gravity stops acting.” Gravity is unchanged; drag simply equals it.
- “Terminal velocity is a fixed number.” It depends on the object, its orientation and the air around it. The same skydiver has different terminal velocities in different body positions.
- “The object reaches it instantly.” It approaches terminal velocity gradually, getting closer and closer without a sharp switch.
Conclusion
Terminal velocity is a neat example of how one added force changes an entire outcome. Take away air and every object falls identically; put it back and shape, size and mass all start to matter. Understanding it makes Newton’s laws feel less like formulas and more like a description of things you can watch happen.
If you would like to build a solid foundation in forces, motion and energy, the free physics courses on Cursa work through these topics with worked examples and everyday applications — a good next step after this one.
