What you Need
What to do
Cut a piece of string that will not quite reach the ground, from about shoulder height.
Tie the mug on one end of the string, and the nut on the other.
Hold the nut in one hand, and the pencil in the other. Put the string over the pencil, and hold the pencil at about shoulder height (with the far end higher than the close end, or the string can fall off!)
Pull the nut away until the mug is near the pencil, and the string is horizontal.
You may want to practise with something less breakable than a mug...
What may happen
You should find that the string wraps itself around the pencil, and the mug doesn't hit the ground.
Why does it happen?
When you let go of the nut, it isn't just pulled towards the pencil, it is also falling downwards under gravity. This means that it starts to rotate around the pencil, like a pendulum. However it is a pendulum which is getting shorter all the time.
When something is rotating around a point, and you move its mass towards the centre of rotation, it will rotate faster. This is because, as the radius of the circle reduces, the distance around the circle that the mass has to travel, decreases - so it takes less time, and the mass rotates quicker. Also as you pull the mass inwards, you do work against what is known as centrifugal force, but is actually the inertia of your mass. This work therefore has the effect of speeding up the mass.
This is the same effect as an ice skater doing an immensely fast spin. When they start, their weight is spread out, but as they pull their weight inwards, they spin faster and faster.
Thankyou to Richard Ellam of LM Interactive for showing me this trick.