Showing posts with label physics. Show all posts
Showing posts with label physics. Show all posts

Friday, 3 July 2015

Mini Blog: Shadows on Celestial Bodies, Umbras, and Umbrellas

I'm going to be starting a series called "Mini Blog", where each post in this series is significantly shorter than the lengthy posts I usually write. In fact, sometimes it may be just a picture. Like this one!

This picture defines umbra, penumbra, and antumbra.

Penumbra in this picture is B, and umbra is A.

The reason why the moon doesn't totally cover up the sun from our perspective on earth during a total eclipse is because the distance between the moon and the earth is around the same distance where the apex of the moon's umbra because of the sun is. Therefore, we see an antumbra instead of a full umbra.

Another fun fact: umbra is the Latin word for shadow. The English word, "umbrella", is also derived from the Latin word "umbra".

Sunday, 10 May 2015

How Cats Always Land on their Feet

My boyfriend recently showed me a gif that he saw on Reddit that startled me initially, as it involved a cat falling from a high building. You'd think the cat would die, but it didn't. It turned itself feet first onto the ground, and scurried away.

You can see the gif here: (Scary, isn't it?)

This blog post will detail the findings my boyfriend and I uncovered whilst researching about how cats always land feet first, and how cats can survive falls from high buildings. Resources that helped aid in this post's information is linked or mentioned throughout this post.

Why don't cats go SPLAT when they fall from a really high building?

Everyone who took physics knows that the reason why we all fall and come back down to earth is because of gravity. That is,

F = mg

The only force trying to resist this force on earth would be air resistance,

Cd  = coefficient of drag (around 0.2)
  ρ  = density of air
  A  = area of object
  v  = velocity of object

Now, you probably know that terminal velocity is basically the maximum velocity a body experiences after X seconds of free falling. This terminal velocity remains the same, or to put it in another way, is constant after X seconds due to the air resistance force and the gravitational force cancelling each other out so that the net F = 0.

During free fall, a cat is usually splaying its body out like a flying squirrel.

When calculating the terminal velocity of the cat, we see that because the cat is splaying its body out, the "projected area" is bigger, so the overall terminal velocity of the cat is smaller. When you actually do experiments, you discover that the terminal velocity of an average cat is calculated to be around 60 mph. Compare that to 120 mph of an average skydiver.

Because of this, cats will generally not die from the force that occurs when landing on the ground. They will not fall to death like a human likely would.

How does a cat always land feet first? (An Explanation of the 'Cat Righting Reflex')

First I would like to explain what angular momentum is, as this is what we need to explain first. Angular momentum is how much an object is rotating, but it depends on the moment of inertia and the angular velocity of the body. It defined in the picture below:

I is the moment of inertia (you can simplify it as the quantity of area away from the axis of rotation), and w is the angular velocity. This picture also shows that angular momentum is the reason why when a ballerina's arms go in, she twirls faster - because angular momentum is preserved. In case (a), I is big because the area around her is big, since her arms are spread out. In the second case, because I is smaller now and L should be constant, w must increase, so she spins faster.

So, now, we should start explaining how a cat actually falls on their feet.

Before photography came into existence (so we could capture frame by frame of how exactly a cat's body orientates itself feet-first to the ground), we thought that a cat flipping feet first was some kind of paradox. This is because it seemed to violate the law of conservation of angular momentum.

This is described in the following youtube video:

A screenshot is below:

As the above screenshot of the video described, it seems that every cat in the world is violating the law of conservation of angular momentum, as angular momentum is always conserved unless an outside force acts upon it.

The only two forces that act on the cat are gravity and air resistance.

Gravity cannot really add or remove angular momentum of the cat, as gravity acts on the center of mass on the cat, which is "in line" with the cat's axis of rotation, so therefore, gravity cannot affect the conservation of the cat's angular momentum. The only other force would be air resistance, but this isn't the correct answer either.

After photographing carefully what cats do when freefalling, we get realize that cats do in fact not violate this law, and do not use air resistance to help conserve angular momentum. But how do they conserve angular momentum, you may ask?

Please click the following gif, as it will explain to you how angular momentum is preserved when a cat is rotating to land feet-first:

A screen shot is here:

After looking at the gif, you can see now how angular momentum is actually conserved! Cats have a very flexible back, so they are able to do these weird rotations of their bodies to orientate themselves upright!

Other fun facts about how cats have 9 lives

How can the cat from the first link I shared in this post survive such a tall height? Read the following from Emily Russell's presentation on "The Physics of Cats" (2007)
A study was released in the Journal of the American Veterinary Medical Association in 1987 of 132 cats which had fallen from high-rise windows in New York. The average fall height was 5.5 stories. 90% of the cats survived. Above a fall height of 7 stories (around 70 feet), the number of injuries the cat sustained actually decreasedThis is because once it has turned over and reach terminal velocity, the cat relaxes its muscles, so that its landing is softer.
Neat, eh? TIL (Today I learned) how cats fall safely to the ground!