illuminating science

For the longest time, I have wondered why you get a “whirlpool” effect when you stir a cup of tea, coffee or whatever you enjoy best. You know - you get it moving with a spoon, and when you take the spoon out, the surface of the water is tilted in towards the centre. As it slows down, the angle of tilt gets narrower until finally your drink is flat and calm again. Though I’ve never sat down and really worked on it, I’ve thought about it several times and never come to a satisfactory conclusion - until I read this site, and their cool “Water Spinner” demo.

The basic idea is that if the whole drink is spinning at the same rate (say, two revolutions per second) then the outside of the coffee must be moving faster than the inside (at the edge of the cup, the drink must travel a much longer distance than the stuff right near the centre, in the time of one full revolution.) But to spin, you need a centripetal force - the force which holds you in the circle and prevents you from flying away. For example, if you’re spinning a ball on the end of a rope, the rope provides the force to keep the ball in the circle. If the rope breaks, the ball flies away.

In the case of the coffee cup, the force comes from gravity and the tilt of the water - the greater the tilt, the stronger the force pulling the coffee into the centre (technically, we’re talking about the horizontal component of the bouyancy force.)

It’s quite easy to show, then, that the surface of the coffee must form a parabola - and would be a good excercise for a first year physics student!

I, for one, feel like a part of me has been completed, and I’ll think I’ll celebrate by booking a couple of tickets to The Producers which is a musical coming to Brisbane in a few weeks!