Most people have heard that cats have nine lives, and this idea is partially do to the
fact that whenever a cat falls from a significant distance they will always land on
their feet and cushion the impact. To answer the question of why cats are able to
twist their entire body while free falling downward we have to look at the concepts
of angular motion.
Historically it has been difficult for physicists to understand why cats do turn over
due to the ideas law of ‘conservation of momentum.’ Angular momentum is defined
by the equation:
L = Iω
‘I’ is defined as the moment of inertia, representing the summation of all forces
resisting the motion and ‘ω’ is defined as the angular velocity. The problem began
due to the fact that when the cats began to fall they would have no initial rotation.
With no external torque or forces, the angular momentum would be 0 and therefore
there would be no rotational velocity, making the ability to turn over impossible.
This theory was disproved when scientists took a better look at what cats do when
they free-fall. The first thing that a cat does is arches its back, into almost a right
angle; this action is significant as it allows the cat to split his body into having two
rotations about different axes. The two different sides of the cat are connected and
moving together, allowing them to have equal but opposite momentums to still
create a net angular momentum of 0 and follow the ‘conservation of momentum’
After the cats arch their backs, they will pull their front paws inward and push their
back paws outward; this will increase the speed of rotation of the cats front and
decrease the speed of cats back in the opposite direction. This can be explained
using the definition of angular momentum and moment of inertia. The moment of
inertia is defined differently depending on the shape of an object, but if we treated
each side of the cat as different point mass:
I = mr^2
‘m’ is defined as mass and ‘r’ is defined as radius. As the cat changes the length of its
legs, the length of its radius will change. Taking the front side of the cats, its leg
length shortens, making r less and therefore producing a lower moment of inertia. If
the moment of inertia is less and the angular momentum remains constant, then the
angular velocity will increase, given the first equation above. Using the same logic
the back legs will indeed slow the backside of the cat down in the opposite direction
in order to equalize the momentums and torques (not external torques so they the
summation of torque should be equal as well in a state of equilibrium).
The final step for the cat is to flip around its previous step. The cat will then pull in
its back legs and push out its front legs, changing the direction of each half and
allowing the back legs to flip around to the correct direction. Being completely
flipped 180° the cat is ready to brace for impact and limit injury.