Let's start with a joke. Do you know the BUTTER CAT PARADOX? It is based on two adages:
cats always land on their feet
buttered toast always land buttered side down
What happens if we attach a buttered toast (butter side up) to the back of a cat while it falls? Will the butter and feet compete for the landing position? Will it reach an anti-gravity position because it rotates fast enough and hover shortly before hitting the ground?
Now back to the real stuff. Cats are always known to be master survivors of jumping from unbelievable heights. These creatures have evolved incredible adaptations and a lot of physics is involved in the few seconds from their fall to their land to save their lives. Though my cat is too fat to ever demonstrate his power as a good physics student to me at home, today I will try to explain the physics involved in falling cats.
The physics
Outside of domestic lives, many cats enjoy a life on the trees hunting, and their bodies are design to deliberately suit their needs when they miss a branch or too and fall down from it. Here are some of their adaptations that is involved:
relatively large surface area compared to their weights
long, compliant legs
flexible body
Firstly, a large surface area is crucial to the cat's landing. When a cat starts to fall, it extends its tail and paws to increase its surface area, and thus increasing air resistance like a parachute. Since the net external force acting on the cat = mass* acceleration, and the force = Fg - Fair (down positive), when there is more air resistance, there is less net force, thus resulting in a smaller acceleration. This allows the cat to reach terminal velocity at a slower speed compared to larger animals such as a human. A man reaches terminal velocity of 197km/h while the cat only has 97km/h, according to 1987 study b y veterinarians Wayne Whitney and Cheryl Mehlhaff. We learned that when there is less velocity and final force, there is less reaction force on the cat to stop it from being crushed.
figure 1: my cat force diagram
Secondly, the cat has springy legs to help divert energy into decelerating rather than harming the body. With a lower velocity, we know that there will be less momentum from the drop since p = mv, and less energy will be acting directly on the muscles and joints. With a bent leg structure and not a perpendicular structure, even less energy is transmitted through the joints and towards the protected areas of the body. The legs also increase the distance that needs to be traveled by the energy compared to a stiff collision, resulting in a longer time of collision. Like how air bags work in a car crash, the leg muscles reduce impact through spreading it over a long period of time.
figure 2: my cat leg diagram
Lastly, a flexible body with all the turning and twisting saves the day. To keep internal torques balanced, when the cat tries to land on its feet before it hits the ground, another part of its body has to turn in the opposite direction and produce the same magnitude of torque. A cat make this possible by splitting its body into two separate rotational axis. Then, the fall follows 4 steps:
through vision or gyro in the ear, determine which way is "up"
pull front legs in to decrease r and moment of Inertia, thus make it spin faster. Extend back legs to increase I and spin slower and balance out torque
Once front legs are positioned, extend them and stop spin. Extend back legs along rear axis to allow fast spin and adjust to face down
extend all legs down, stop spinning and brace for landing
figure 3: my cat spin diagram
An extremely flexible body allows the cat to twist and adjust to a good landing position and protect itself from dying. However, it is still highly likely for the cat to suffer internal organ damage and a broken jaw. For safety reasons, LOOK AFTER YOUR CAT PLS.