Free Fall and Gravity — The Complete Physics Guide
Free fall is the motion of an object under the influence of gravity alone, with no air resistance or other forces acting. It is the purest expression of gravitational acceleration — every object in free fall, regardless of mass, accelerates at exactly the same rate near the Earth's surface: g = 9.81 m/s². This remarkable fact, first demonstrated by Galileo in the late 16th century, overturned two thousand years of Aristotelian physics and paved the way for Newton's universal theory of gravitation.
The Constant of Gravitational Acceleration
Near the Earth's surface, the gravitational field strength is approximately 9.81 N/kg, which means every kilogram of mass experiences a downward force of 9.81 newtons. By Newton's Second Law (F = ma), this produces an acceleration of 9.81 m/s² regardless of mass — because the gravitational force is proportional to mass, and F = ma means a = F/m = g × m/m = g.
The value g = 9.81 m/s² is an average for Earth's surface. In reality, g varies slightly with latitude (it is slightly larger at the poles than at the equator due to Earth's rotation and shape) and altitude (decreasing as 1/r² with distance from Earth's centre). At the top of Mount Everest, g ≈ 9.77 m/s². For most problems, g = 9.81 m/s² is used, though some textbooks and examiners use the approximation g = 10 m/s² for simplicity.
On other planets and the Moon, the equivalent value differs significantly. On the Moon, g ≈ 1.62 m/s² — about 1/6 of Earth's value. This is why the Apollo astronauts could jump so high and why objects fell so slowly in the famous lunar footage. On Mars, g ≈ 3.72 m/s², on Jupiter g ≈ 24.8 m/s², and on the surface of a neutron star g can exceed 10¹² m/s².
Free Fall Equations
Free fall is simply vertical motion under constant acceleration g. The SUVAT equations apply directly, with a = g downward:
For an object dropped from rest (u = 0), these simplify to: v = gt, h = ½gt², and v = √(2gh). These three forms are the most commonly used in problems — you should be comfortable deriving any one from the others.
Worked Example 1 — Time to Hit the Ground
Problem: A stone is dropped from a bridge 78.4 m above a river. How long does it take to hit the water, and what is its speed at impact?
Time: h = ½gt² → 78.4 = ½ × 9.81 × t² → t² = 78.4/4.905 = 15.98 → t = 4.0 s
Speed at impact: v = gt = 9.81 × 4.0 = 39.2 m/s (about 141 km/h)
Worked Example 2 — Object Thrown Upward
Problem: A ball is thrown vertically upward with initial speed 15 m/s. Find the maximum height and the total time before it returns to the thrower's hand.
Max height (at v = 0): v² = u² − 2gh → 0 = 225 − 2 × 9.81 × h → h = 225/19.62 = 11.47 m
Time to peak: v = u − gt → 0 = 15 − 9.81t → t = 1.53 s
Total time (symmetry — same time down as up): T = 2 × 1.53 = 3.06 s
Terminal Velocity and Air Resistance
True free fall — with zero air resistance — is an idealisation. In reality, any object moving through air experiences drag, a resistive force that depends on speed, cross-sectional area, shape, and air density. As a falling object accelerates, drag increases until it equals the gravitational force. At this point, net force is zero, acceleration stops, and the object falls at constant terminal velocity.
Terminal velocity varies dramatically with object properties. A skydiver in a belly-down position reaches about 55 m/s (200 km/h). In a head-down dive, terminal velocity increases to around 90 m/s (320 km/h). A feather reaches terminal velocity almost instantly at less than 1 m/s. A steel ball bearing has a terminal velocity far higher than a human being reached from most practical heights.
The famous "feather and hammer" demonstration — dropping both objects simultaneously in a vacuum — shows identical acceleration and identical impact times, confirming that air resistance, not mass, is responsible for their different fall rates in everyday conditions. Apollo 15 astronaut David Scott performed this exact experiment on the lunar surface in 1971.
Applications of Free Fall Physics
Roller coasters: The initial drop of a roller coaster is essentially free fall (with the track constraining the direction). The maximum speed at the bottom of a drop of height h is v = √(2gh) — the same formula as free fall. A 40 m drop gives a speed of about 28 m/s (100 km/h).
Drop testing: Engineers use free fall to test the impact resistance of products — smartphones, packaging, aircraft components. Dropping from a known height gives a precise impact velocity via v = √(2gh), allowing consistent, reproducible tests.
Orbital mechanics: Objects in orbit are in a state of continuous free fall — they are always falling toward Earth, but their horizontal velocity is high enough that Earth's surface curves away beneath them at the same rate. The ISS orbits at about 400 km altitude and falls toward Earth at the same rate it moves forward, resulting in a stable circular orbit. Free fall and orbital mechanics are the same physics at different scales.
Galileo and the History of Free Fall
Before Galileo, Aristotelian physics held that heavier objects fall faster than lighter ones — a belief so intuitive that it went unchallenged for nearly two thousand years. Aristotle reasoned that a 10 kg stone should fall ten times faster than a 1 kg stone because it is ten times heavier.
Galileo demolished this view through careful experiment, most famously (though possibly apocryphally) by dropping two cannonballs of different masses from the Leaning Tower of Pisa. More rigorously, he used inclined planes to slow down the motion enough to time it with water clocks, demonstrating that distance fallen is proportional to the square of time — the signature of constant acceleration — and that this acceleration is the same for all masses.
Newton later explained why: gravitational force is proportional to mass (F = mg), and by F = ma, the mass cancels out, giving a = g for all objects. The equivalence of inertial mass and gravitational mass — the fact that the same property (mass) determines both resistance to acceleration and response to gravity — is one of the deepest puzzles in physics. Einstein elevated it to a postulate in his General Theory of Relativity, where it becomes the equivalence principle: a gravitational field and an accelerating reference frame are locally indistinguishable.
Precise modern experiments using laser interferometry have confirmed that the gravitational and inertial masses of various materials agree to better than one part in 10¹². This extraordinary precision makes free fall one of the most precisely tested areas in all of physics.
Free Fall in Microgravity
Astronauts aboard the International Space Station appear to float — but they are not in zero gravity. The ISS is in a state of continuous free fall around Earth. Both the astronauts and the station are falling toward Earth at the same rate, so there is no relative motion between them — they appear weightless relative to each other and their surroundings.
True zero gravity exists only infinitely far from any mass. What we call "microgravity" aboard spacecraft is actually free fall — and it has profound physiological effects on the human body. Without the need to support body weight against gravity, muscles atrophy, bones lose density, and fluid redistribution changes cardiovascular function. ISS crew exercise two hours daily to counteract these effects.
Drop towers — vertical shafts up to 150 metres tall — are used on Earth to study free fall for short periods. The Bremen Drop Tower in Germany provides 4.7 seconds of free fall, during which experiments experience microgravity conditions. Parabolic aircraft flights (the "vomit comet") provide about 25 seconds of free fall per parabola. These facilities allow researchers to study fluid behaviour, combustion, and biological processes in free fall conditions without the cost of orbital spaceflight.