In 2018, a remarkable news story came out of New York City: a cat fell from the 32nd floor of an apartment building and hit the asphalt below. Shockingly, despite sustaining a collapsed lung and broken teeth from the high fall, the cat survived without any life-threatening injuries. This four-legged friend only needed two days of treatment at the vet before being able to go home. Similar stories of cats surviving falls have happened many times, leading to the popular saying, “Cats have nine lives.” For decades, researchers from various fields have been trying to understand: how do cats possess such incredible survival skills?However, in the late 19th century, what initially confused physicists was not the fact that cats could survive falls from dizzying heights. Instead, what baffled them were a series of photographs showing how cats rotate their bodies mid-air and land on their feet. These images revealed an unusual phenomenon: a person would grab the cat’s legs, let go while the cat’s back was facing the ground, and the cat would fall. In the first part of the fall, the cat would be upside down, with its back facing the ground. But in the second part of the fall, something seemed to defy the laws of physics: the cat flipped over and landed on all fours.
-
Defying the Laws of Physics?
In our daily lives, we can observe that these four-legged animals are able to rotate in mid-air. According to the law of conservation of angular momentum, an object that isn’t rotating initially cannot start rotating on its own without an external force. For a long time, people thought that the rotational momentum of cats in mid-air came from the force they exerted to push themselves off the plane when they fell. However, the photographs showing this phenomenon contradicted that idea. Initially, the cat fell straight down, but then somehow it managed to rotate around its own axis. How was this possible? Many scientists have tried to explain the “falling cat” phenomenon, including James Clerk Maxwell, the father of electromagnetism, who conducted a series of experiments with cats falling from different heights (including from open windows) onto beds and tables. But it wasn’t until 1969 that the mystery was solved.It turned out that our observations of a cat’s body had been too simplistic. It wasn’t simply a cylindrical object that rotated once it was airborne. Upon closer inspection, you may notice that during the fall, the cat’s upper and lower body rotate in different directions, ensuring the conservation of angular momentum throughout the process. It’s similar to a pepper grinder: the cat’s body divides into two sections, each rotating in opposite directions, which keeps the total angular momentum at zero. But how does a cat ensure it lands on its feet? The answer is that cats are physics masters! They cleverly use the principles of classical mechanics: by pulling their front legs close to their body, like a figure skater reducing rotational inertia, the upper body rotates quickly around its own axis. For the rear legs, however, they do the opposite—stretching them out to increase rotational inertia. This allows the upper body to rotate a larger angle while the back legs only need to rotate a small angle in the opposite direction. (Thankfully, cats have extremely flexible spines!) Once the cat’s upper body is in the correct position (with its head facing the ground), it can extend its front paws, contract its hind legs, and rotate in the opposite direction, just like grinding pepper, until its rear paws are aligned with the ground. Through this technique, cats always manage to land on all fours—without violating any laws of physics.
-
From What Height Can a Cat Survive a Fall?
Physics dictates that the higher an object falls from, the greater the impact force. However, a study in the 1980s discovered an unusual pattern—at least for cats. In this study, two veterinarians in New York City documented 132 incidents of cats falling from windows between June and November of 1984. Most of these cats fell from about 32 stories high, and overall, 90% of them survived. When the veterinarians recorded the extent of the cats’ injuries, they came to a surprising conclusion: below seven stories, the severity of injuries increased with height, but above seven stories, the injuries seemed to decrease. In other words, falling from the sixth floor was actually more dangerous than falling from the 11th floor. It seemed like once again, cats were defying the laws of physics.When a cat falls from greater heights, it has more time to accelerate under the force of gravity, meaning it should be falling faster and faster until it hits the ground. The sudden impact could cause bone fractures, lung collapse, or even worse outcomes. In theory, the higher the fall, the worse the consequences. However, considering the cat’s free fall, we often overlook the effect of air resistance. After all, cats aren’t falling in a vacuum—they’re falling through air, which can slow them down. In fact, as a cat falls, two opposing forces act on it: gravity and friction. The friction force slows it down. In an ideal situation with no air resistance, calculating gravity is simple—just multiply the cat’s mass by gravitational acceleration. But air resistance depends on the object’s cross-sectional area, drag coefficient, air density, and velocity. When a cat first begins to fall, its speed is zero, so only gravitational acceleration is acting on it. As the cat’s speed increases, the opposing friction force kicks in. To understand the cat’s motion, we must calculate the net force (gravity – friction), and the net force determines the object’s acceleration and direction.
-
The Cat’s Terminal Falling Speed
But after a cat falls for a while, its speed will increase until the friction force equals the gravitational force. At that point, the net force becomes zero. Of course, this means acceleration will also be zero. No further acceleration means that the cat’s speed won’t increase any more—it has reached its terminal velocity. You can easily calculate this maximum speed. Since terminal velocity occurs when friction and gravity are balanced, with these two forces cancelling each other out, the object falls at a constant speed. Assuming the cat weighs 4 kilograms and is about 50 cm long and 15 cm wide, we can estimate the cat’s cross-sectional area to be 0.075 square meters. From these parameters, assuming the cat is a cylindrical object, we can calculate the terminal velocity to be 32.68 meters per second, or just under 120 kilometers per hour. From the graph, we can see that at a 100-meter fall, the cat’s speed reaches 30 meters per second. Since we have observed cats surviving falls from much higher buildings (like the 32nd floor), they should be able to survive impacts at a speed of 120 kilometers per hour. Therefore, theoretically, cats might survive falls from almost any height.
-
The Survival Bias of Cats?
However, this calculation of a cat’s terminal velocity doesn’t explain the observation made by the New York veterinarians: why do cats have a higher survival rate when falling from the 7th floor or higher compared to falling from lower floors? After all, the impact speed is lower from the lower floors, so the impact force should be smaller. One explanation involves the animal’s experience. When a cat falls from a lower height, it may be in a state of free fall for a short period. Therefore, instinctively, the cat will extend its legs and land on its feet. However, when falling from higher heights, this strategy doesn’t work as well: because of the cat’s uneven weight distribution, extending its legs could cause serious injury. This difference might explain why survival rates decrease with height when falling from below the 7th floor. On higher falls, friction becomes more significant, and the cat no longer feels as though it’s falling. It relaxes, no longer stretching out its legs. Its weight distribution becomes more balanced, and the landing is smoother, increasing its chances of survival.
This difference might explain why survival rates decrease with height when falling from below the 7th floor. On higher falls, however, friction becomes more significant during the descent. Veterinarians speculate that, at greater heights, the cat no longer feels like it’s falling. Instead, it becomes more relaxed and doesn’t extend its legs. This allows its weight distribution to become more balanced, and the landing is much smoother, significantly increasing its chances of survival.
