What happens when you hurl your homework in the air?

This week Derek is with Professor Hugh Hunt from the University of Cambridge and three student volunteers from the Norwich School. They're going to be throwing books into the air and learning about the science of spin.

To do the experiment, you will need:

- A rectangular (preferably hardback) book

- An elastic band to hold the pages together 

How to do the experiment:

1 - Take the book and put the elastic band around it to keep the pages together. 

2 - Hold the book in your hands so that the book is flat and the spine is facing away from you. 

3 - Throw the book up into the air and make it spin so that the spine moves towards you and then away again. Catch the book and see if it looks any different. 

4 - Now hold the book so that it is flat between thepalms of your hands with the spine facing away from you. Spin the book again, aiming to make the spine come towards you and away again. Look again at the position of the book once you've caught it. (Don't worry if youcan't see any difference in stages 3 and 4!) 

5 - Now hold the book as though you were looking atthe cover ready to read it. The spine should be on the left hand side. Throw it up into the air and make itspin. What changes about the position of the book? How has the cover changed relative to how it was before you threw it?   

What's going on?

In steps 3 and 4, nothing particularly remarkable happens! They spin about the same axis all the way through and land in your hands in the same orientation.  However, when you throw it in step 5, it should have landed in pretty much the same way but rotated round 180 degrees. You will have noticed this because the front cover should be upside down. Anybody watching you throw the book will see that it starts going up normally and spinning but then does a flip when it gets to the top.  So what's happening?

When you throw it up into the air, the book starts spinning as you would like it to spin, but it doesn't last long! It turns out that spin about this particular axis is unstable, and doesn't like to spin in the way you would expect for very long. This makes the book start to tumble out of control. Once it's done this flip, it magically starts spinning nicely again, but the other way round. This means that, when you finally catch the book, it's lying in your hands upside down. 

This is all rather different to the other two ways of spinning the book. These two spin directions are what we call stable. You can think of this by imagining holding a pencil by its tip. If you hold the pencil so that the rubber is pointing downwards, it won't move. In fact, you could hold it like that for hours because gravity is forcing downwards and the direction is stable.

In contrast, if you try to balance a pencil on your finger tip with the rubber pointing upwards, the direction is unstable and the pencil falls down.  You can imagine that this pencil is a little bit like a pendulum. When it's swinging backwards and forwards down the bottom, then it's a stable situation. But if you imagine tipping it right up around 180 degrees, it wouldn't stay there for very long. It would swing down, go right the way round and come back to the top again.

So if it fell to the right, it comes back again from the left. Instabilities quite often involve moving away from where you started and coming back again the other way round. This is why the book turns 180 degrees from its original position. However, if you throw it again, the flip turns the book in the opposite direction and brings you back to the beginning. 

If you toss the book up high enough, it might do two flips. This will make it come back into your hands with the cover in the same orientation as before you threw it. 

These same spinning stabilities and instabilities can be seen in objects such as mobile phones because they're the same shape as books (one long axis, one medium axis and one short axis). Even a cat falling out of a tree uses the same principles to move itself around.