### Question

How does a cat land on its legs when dropped?

Cats have the seemingly unique ability to orient themselves in a fall allowing them to avoid many injuries. This ability is attributed to two significant feline characteristics: A ï¿½righting reflexï¿½ and a unique skeletal structure.

The ï¿½righting reflexï¿½ is the catï¿½s ability to first, know up from down, and then the innate nature to rotate in mid air to orient the body so its feet face downward. Animal experts say that this instinct is observable in kittens as young as three to four weeks, and is fully developed by the age of seven weeks.

A catï¿½s ï¿½righting reflexï¿½ is augmented by an unusually flexible backbone and the absence of a collarbone in the skeleton. Combined, these factors allow for amazing flexibility and upper body rotation. By turning the head and forefeet, the rest of the body naturally follows and cat is able reorient itself.

Reports of cats surviving falls of several stories in height have coined the expression of cats having ï¿½high rise syndrome.ï¿½ Like many small animals, cats are said to have a non-fatal terminal falling velocity. That is, because of their very low body volume-to-weight ratio these animals are able to slow their decent by spreading out ï¿½ flying squirrel style. Simply put, animals with these characteristics are fluffy and have a high drag coefficient giving them a greater chance of surviving these falls.

Answered by: Stephen Portz, Technology Teacher, Space Coast Middle School, FL

Moment of inertia is important ...

To understand how a cat can land on it's feet, you must first understand some concepts of rotational motion, since the cat rotates as it falls.

Rotational motion is similar to motion in a straight line (linear motion), however the constants are slightly different. For example, instead of the mass of an object, we use what is known as the moment of inertia.

The moment of inertia of an object is determined by the distance it's mass is distributed from the rotational axis. Think of a ball tied to a string that you swing around your head, the greater the length of the string, the greater the object's moment of inertia. Relating this to the cat, if the cat stretches out it's legs and tail, it increases it's moment of inertia; conversely, it can decrease it's moment of inertia by curling up. You can prove this by extending your arms while spinning around on a swivel chair.

Just as a more massive object requires more force to move, an object with a greater moment of inertia requires more torque (which is the angular equivalent of force, and is proportional to the distance from the axis of rotation) to spin. Therefore by manipulating it's moment of inertia, by extending and retracting its legs and rotating its tail, the cat can change the speed at which it rotates, giving it control over which part of it's body comes in contact with the ground.

... and the conservation of angular momentum ...

If a cat is dropped they almost always tend to land on their feet because they use the conservation of angular momentum to change their orientation. When a cat falls, as you would expect, its centre of mass follows a parabolic path. The cat falls with a definite angular momentum about an axis through the catï¿½s centre of mass. When the cat is in the air, no net external torque acts on it about its centre of mass, so the angular momentum about the cats centre of mass cannot change. By pulling in its legs, the cat can considerably reduce it rotational inertia about the same axis and thus considerably increase its angular speed. Stretching out its legs increases its rotational inertia and thus slows the catï¿½s angular speed. The conservation of angular momentum allows the cat to rotate its body and slow its rate of rotation enough so that it lands on its feet safely.

### Science Quote

'I have deep faith that the principle of the universe will be beautiful and simple.'

Albert Einstein
(1879-1955)