What happens when you hurl your homework in the air?

01 October 2006

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 the

palms 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 you

can't see any difference in stages 3 and 4!)

5 - Now hold the book as though you were looking at

the cover ready to read it. The spine should be on the

left hand side. Throw it up into the air and make it

spin. 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 bus 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 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.

Want to find out more?

There are hundreds of other interesting facts and a

whole host of science behind spinning objects. To find

out more and to see video footage of some similar experiments,

you can go to Hugh

Hunt's website.

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