Coriolis force

In physics, the Coriolis force is a special kind of force that affects objects moving on a rotating surface. Because our Earth spins, things like air and water don’t move in straight lines. Instead, they curve. This curving effect is called the Coriolis effect.

The Coriolis force acts to the left of moving objects on Earth in one direction and to the right in another. Specifically, in the Northern Hemisphere, objects are pushed to the right, while in the Southern Hemisphere, they are pushed to the left. This is why big weather patterns, like cyclones, spin the way they do.

This force is very small for everyday things but becomes important over large distances and long times, like in big storms or ocean currents. It helps explain why winds and water move in curves rather than straight lines across our planet.

History

Italian scientist Giovanni Battista Riccioli and his assistant Francesco Maria Grimaldi talked about this effect in 1651 when discussing artillery. They said that because the Earth spins, a cannonball fired north would move to the east. In 1674, Claude François Milliet Dechales also described how Earth's rotation could change the path of falling objects and projectiles.

Later, Gaspard-Gustave de Coriolis wrote a paper in 1835 about machines with moving parts, like waterwheels. He described forces that appear in spinning frames of reference. By 1920, this effect was called the "Coriolis force." In 1856, William Ferrel suggested that this force helps create the prevailing westerly winds by affecting air movement.

Formula

See also: Fictitious force

In simple terms, when something moves in a spinning area, it seems to feel an extra push. This push is called the Coriolis force.

If the area spins clockwise, this push seems to come from the left. If the area spins counterclockwise, the push seems to come from the right. The push depends on how fast the object is moving and how fast the area is spinning.

The Coriolis force only matters if the object is moving at an angle to the spin axis. If the object moves straight along the spin axis, there is no extra push. If it moves straight toward or away from the axis, the push will be in the direction of the spin or opposite to it, respectively.

Intuitive explanation

Imagine an object moving north on the ground in the Northern Hemisphere. From space, the object doesn’t just go straight north. It also moves east because the Earth rotates. As the object moves farther north, the ground below it spins more slowly. The object keeps moving east at the speed it had when it started, so it ends up leaning to the right of its original path.

This sideways push happens no matter which way the object is moving, not just north. Scientists have shown that this effect is too tiny to change the way water spins down a drain in a bathtub or sink. Other forces are much stronger and control that movement.

Length scales and the Rossby number

Further information: Rossby number

The size, speed, and time of a moving object help us understand how important the Coriolis force is. We can figure this out using something called the Rossby number. This number tells us how the object's speed compares to the spinning of the Earth and the distance it travels.

If the Rossby number is small, the Coriolis force has a big effect. If it's large, other forces are more important. For example, in tornadoes, the Rossby number is large, so the Coriolis force doesn't matter much. But in big weather systems, the Rossby number is small, and the Coriolis force plays a big role. In oceans, the Rossby number is often around 1, meaning all forces are important.

For example, a weather system moving at 10 meters per second over a distance of 1,000 kilometers has a Rossby number of about 0.1.

Long-range missiles and shells can be affected by the Coriolis force. In the Northern Hemisphere, they land to the right of their target, while in the Southern Hemisphere, they land to the left. This was one of the first things that made scientists notice the Coriolis force.

Simple cases

Tossed ball on a rotating carousel

The figures show a ball thrown from the top of a spinning carousel toward its center. When seen from above, the ball moves slightly to the right of the center because it already had some sideways speed from the spin and the throw. In the view of someone spinning with the carousel, the ball curves a little.

Bounced ball

The figure shows a more detailed case where the ball thrown on a turntable bounces off the edge and returns to the thrower. The path looks different depending on who is watching. For someone spinning with the turntable, the ball makes a big curve going out and a straighter path coming back. For a person standing still, the ball moves in straight lines the whole time.

Applied to the Earth

The movement of air sliding over Earth's surface is affected by a special force. This force depends on how fast Earth spins and where you are on Earth.

In places north of the equator, this force pushes moving objects to the right. In places south of the equator, it pushes them to the left.

Rotating sphere

When we think about a point on Earth spinning around its axis, we can imagine a tiny coordinate system at that point. This helps us understand how the spinning affects moving things.

Meteorology and oceanography

The spinning of Earth has a big effect on big movements of air and water. It helps create swirling patterns in oceans and can influence weather systems.

Flow around a low-pressure area

Main article: Low-pressure area

When low pressure forms in the air, air moves toward it but gets turned sideways by Earth's spin. This creates circular movements in weather patterns.

Inertial circles

An air or water mass moving only under the influence of Earth's spin travels in a circular path called an inertial circle. The size of this circle depends on how fast the Earth spins and how fast the air or water is moving.

Other terrestrial effects

Earth's spin affects large-scale air and water movements, creating patterns like jet streams and ocean currents.

Eötvös effect

Main article: Eötvös effect

Objects moving east or west on Earth feel a slight upward or downward pull because of Earth's spin. This effect is strongest near the equator.

Intuitive example

Imagine a train moving around the world along the equator. Depending on whether it moves east or west, it would feel slightly heavier or lighter because of Earth's spin.

This also explains why objects fired westward fall slightly lower and those fired eastward fall slightly higher.

Draining in bathtubs and toilets

Contrary to popular belief, bathtubs, toilets, and similar containers don't drain differently in the Northern and Southern Hemispheres. The force from Earth's spin is too tiny to affect small drains. The shape of the drain and the water's starting motion have much bigger effects.

Laboratory testing of draining water under atypical conditions

In very careful experiments, scientists have shown that under perfect conditions, water can spin slightly because of Earth's spin. But in everyday sinks and tubs, this effect is too small to notice.

Ballistic trajectories

The spin of Earth can change the path of very long-range projectiles like artillery shells. Snipers and gunners must account for this to hit their targets accurately over long distances.

Visualization

To show the Coriolis effect, we can use a special round table that spins. If the table is flat, objects will slide off because of their natural motion. But if the table is shaped like a bowl and spins at the right speed, we can see the Coriolis effect clearly.

We can use pieces of dry ice as objects that move easily on the table. By filming the motion from a camera that spins with the table, we can see how things move from the table's perspective. From a stationary view, the objects move in oval paths due to gravity. But from the spinning view, the objects move in circles because the forces balance out, and the Coriolis effect becomes visible.

Because the table spins much faster than the Earth, the Coriolis effect is stronger and easier to see in a short time. This helps us understand how the Earth's rotation affects movement, similar to how the spinning table works. The Earth's shape and forces also balance in a way that lets us observe effects like the motion of a Foucault pendulum.

Main article: Foucault pendulum

In other areas

Coriolis flow meter

The Coriolis effect is used in special tools called mass flow meters. These tools measure how much liquid is moving through a pipe and how thick the liquid is. They work by shaking the pipe slightly and watching how the liquid moves inside. This shaking creates a spinning motion that helps the tool figure out the flow and thickness of the liquid.

Molecular physics

In molecules made of many parts, the parts can both spin and shake. Because of this shaking, the parts move in ways that mix spinning and shaking motions. This mixing helps scientists learn more about how the molecule is built.

Insect flight

Some flies and moths use the Coriolis effect to help them fly. They have special parts on their bodies that can sense when they turn. Flies have tiny dumbbell-shaped parts near their wings called halteres, and moths use their antennae for this purpose. These parts help the insects know when they move sideways, up and down, or twist.

Lagrangian point stability

In space, there are special spots where small objects can stay in place between two bigger objects, like planets or stars. These spots are called Lagrangian points. The Coriolis effect helps keep these spots stable, allowing small objects to orbit around them in special paths.