The Coriolis effect.

Step 1 of 8

A throw that misses

Two children stand on a turning carousel, one at the middle and one at the rim. The one in the middle throws a ball straight at the other. In the Unit on circular motion we saw that a body keeps going in a straight line unless a force turns it. In the Scene the carousel stands for the ground at one Latitude of a spinning planet, and each throw stands for $3$⁠ hours of planet time. No motor drives the carousel: it turns because the planet beneath it does.

Step 2 of 8

Right in the north, left in the south

Ride along is at Riding along: the camera turns with the ground. The carousel seems to stand still, and the ball’s chalk trace curves. This is the Coriolis effect: a bend seen only by someone turning with the ground. In London, at 51.5° north, the ball lands to the right of the catcher.

Step 3 of 8

The sine of the latitude

At the North Pole the ground turns about its own upright just like a carousel, a full turn a day, anticlockwise seen from above. At the equator the ground is carried round the Earth’s axis but does not turn about its own upright at all: a line painted on it north–south stays north–south. In between, the ground turns at the Earth’s rate times the sine of the latitude, $\sin\varphi$⁠:

$n_{\text{ground}} = n_{\text{planet}} \sin\varphi$$n_{\text{ground}} =$$n_{\text{planet}} \sin\varphi$⁠

Here $n$⁠ is the number of turns a day. The Latitude and Rotation rate are locked, and the label that prints the bend has been hidden.

Step 4 of 8

Finding a latitude

The ball lands as far round from the catcher as the angle the ground turned during the flight. At a pole, on a 3-hour throw, that is an eighth of a turn, 45°. The Latitude is now at the Equator, where the ball lands in the catcher’s hands.

Step 5 of 8

Foucault’s pendulum

In 1851 Léon Foucault hung a heavy pendulum from the dome of the Panthéon in Paris. Its plane of swing stayed fixed relative to the stars, and the floor turned beneath it, so the pendulum seemed to turn slowly. It is the same turning ground and the same rule: the Earth’s rate times $\sin\varphi$⁠. The label in the Scene shows that rate in Jerusalem.

Step 6 of 8

Spinning storms

Step Ride along to Winds and storms: the carousel draws back until it is a speck on a globe. A storm is a patch of low pressure that draws air in from all sides. Each stream of air is bent to the right in the north, misses the centre and swings round it anticlockwise; in the south it is bent to the left, and storms turn clockwise. The same bend turns the air flowing towards the equator into the trade winds, which blow from the north-east and the south-east.

Step 7 of 8

The sink myth

The Coriolis effect is very weak over short times: a baseball thrown 60 m in two seconds moves sideways by less than a centimetre. It grows with the square of the time in flight, so it matters for anything that keeps moving for hours and days.

Step 8 of 8

On Jupiter

Jupiter spins two and a half times as fast as the Earth, so its winds curve far more: they are drawn out into bands along the latitudes, and its storms turn for centuries.