## Thursday, December 3, 2015

### Why do cats always land on their feet?

By Piper McCabe

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’

law.

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.