Coriolis effect

The effect caused by the Earth's rotation, which causes other things on its surface to tend to turn. This effect acts at a right angle to an object's direction of motion, deflecting the object to the right in the northern hemisphere, and to the left in the southern hemisphere. There is no coriolis effect at the equator. The coriolis effect affects wind, ocean currents, the launching of spacecraft, storm circulation (such as hurricanes and tropical storms), and even the routes taken by jets and airplanes.

Contrary to popular belief, the Coriolis effect has almost no effect on the direction in which water rotates as it drains from your sink or toilet.

The reason it affects the rotation of storms is due to the massive size of weather systems. A hurricane, for example can be several hundreds of kilometers in diameter. This means that one end of the storm is significantly closer to the equator to the other. Because of the fact that the surface of the Earth is moving faster at the equator than at areas to the north or south of it, large systems such as hurricanes tend to rotate. The direction of the rotation is counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. As you can no doubt see, the distance to the equator does not differ significantly between the north and south ends of your typical sink. The Coriolis effect, while present, is immeasurably small in this case.

The direction in which the water rotates is governed by much stronger local variables, such as the shape of the sink and the direction from which the water is flowing into it. Ditto for the toilet. You can prove this to yourself in a large public rest room. If you fill several similar sinks with water and then pull the plugs on all, chances are that in at least one the water will be rotating in a different direction than in the others.

Along the lines of El Puerco Loco facts about the minute impact the coriolis effect has on toilets and sinks is a nifty little trick that clever noders can use as one of the many ways to prove that your physics teacher is a dumb ass.

Write a report on the Coriolis effect, and as your demonstration (which many teachers have begun to employ as a way to discourage plagiarism) offer to prove to the class that you are God. As evidence to your divinity, you will manipulate gravity, one of the most fundamental and powerful forces of the physical world.

Take a plastic bucket or other expendable water receptacle and put a cork in the bottom. Use tape to divide the classroom into two "hemispheres." Point out that, according to the physics we all learned from The Simpsons, toilets will flow counter-clockwise in the northern hemisphere and clockwise in the southern hemisphere. Place a bucket or bowl on each hemisphere as well, to give you something to "flush" into.

Walk around the class to show everyone your experimental toilet. Be sure to only make right turns. This will make the water flow in a clockwise motion. Go to the "northern hemisphere" and pull the cork (i.e. flush the toilet). You have just defied gravity. Repeat, making only right turns, for the southern hemisphere. Then explain that The Simpsons is not a reliable source of physics information, and that you are really not a deity. It is an impressive demonstration, worth an A in most high school science classes.

The Coriolis effect is a phenomenon that is observed by observers in rotatating frames of reference.

Let S be an inertial frame of reference, and S' a frame that is rotating with respect to S. Let r denote a position vector. This will be the same in both frames. Further, let (r')_S, (r')_S', (r'')_S, (r'')_S' denote the velocity and acceleration of r as measured in S and S' respectively.
As a consequence of Euler's theorem there is an angular velocity w such that (r')_S = (r')_S' + w x r, where x denotes a vector product. Using this no less than three times we get

(r'')_S = ((r')_S')_S = ((r')_S')_S' + w x (r')_S = ((r')_S' + w x r)')_S' + w x ((r')_S' + w x r) = (r'')_S' + 2w x (r')_S' + w x (w x r)

(where we have assumed w constant, since this holds in most of the applications we are interested in). If r is the position vector of particle of mass m, acted upon by a force F, then

F = m(r'')_S = m(r'')_S' + 2mw x (r')_S' + mw x (w x r)

which can be rewritten as

m(r'')_S' = F - 2mw x (r')_S' - mw x (w x r)

Thus to an observer in S'' there appear two pseudo forces: the centrifugal force -mw x (w x r) and the Coriolis force -2mw x (r')_S'
With all the cross products in can be a bit difficult to interpret those expressions. The result is that if r_w, is the component of r perpendicular to w, and r, w have magnitudes r, w then the centrifugal force is mw²r_w directed outwards from the axis of rotation, and the Coriolis force is 2mwr', directed at a 90° angle to the direction of motion.

Earth itself is a rotating frame of reference, with an angular velocity w = 2π/24h. The centrifugal force is not particularly interesting, since it is practically constant and is 'absorbed' by gravitation. The Coriolis effect is noticable though.
Suppose an object is moving at speed v on the surface of the Earth on the northern hemisphere at latitude L. Then component of the coriolis force acting on the object along the surface of the Earth is 2mwv*sin L, and it is directed to the right with respect to the direction of motion. On the southern hemisphere sin L is negative, so the object is deflected to the left instead.
On the equator sin L = 0, so an object moving along the surface of the Earth there does not experience any Coriolis force. This is not the same thing as saying that the Coriolis effect vanishes there; a falling onject is deflected to east by a force 2mwv*cos L, and this effect is in fact greatest at the equator!

The Coriolis effect is particularly noticable in eg the weather. If there is an area of low pressure air moves in towards the centre. The motion is deflected to the right (on the northern hemisphere), and the result is that the air moves counterclockwise around the origin. If there is a high pressure the effect is reversed.

The impact of the Coriolis effect on a fluid flow depends on the dimensionless Rossby number R₀ = U/fL, where U is the velocity scale of the system, L is the length scale and f is the Coriolis parameter. Coriolis effects are significant for R₀ << 1 and insignificant for R₀ >> 1. The reason why the weather but not your sink is affected by the Coriolis effect is therefore not that the sink is smaller, but that the ratio of length to velocity is smaller in the sink.

The Coriolis Force is an inertial pseudoforce (not a real force -- it's just pretending. Like the so-called centrifugal force) and is an effect of the noninertial reference frame of an object that rotates at constant angular speed ω. As an example, we will consider a man at point B (near the edge of a large circle) and a woman at point A (closer to the centre), point A being a distance of r_A from the centre, O, and B being a distance of r_B away. The circle is rotating with angular velocity ω. If A throws a ball to B, the ball will have velocity not just towards the location of B when the ball was thrown, but also a velocity vector perpendicular to that, v_A. v_A must equal r_Aω, but it turns out that the man will not be able to catch the ball, because his own velocity, v_B (r_Bω), is greater than v_A, because, as was said earlier, r_A is less than r_B.

Now, let's look this over taking the spinning circle as our frame of reference. From this standpoint, A and B are not moving at all, and A throws the ball to B with velocity v towards B. However, due to the reasons stated in the previous paragraph, it appears as if the ball is attracted to the right and passes by A. It is as if a force is pulling the ball, perpendicular to v. This force creates an acceleration known as Coriolis acceleration, due to a non-existant force known as The Coriolis Force.

After a bit of arithmetic, too long to detail here (See if you can figure it out! Start out with r_B - r_A = vt.), we get the following equation that describes, Coriolis acceleration, a_cor

a_cor = 2ωv

The Coriolis Force has several interesting effects on Earth. Without it, air would be sucked directly into a region of lower pressure, but due to the Coriolis force, the winds appear to be deflected to the right and swirl around a low pressure area instead (clockwise in the Southern Hemisphere, counterclockwise in the Northern Hemisphere). This is why cyclones rotate in opposite directions depending on whether you are north or south of the equator. The Coriolis Force also explains the easterly trade winds near the equator. Also, an object falling from a height will be deflected slightly to the East, because of the Coriolis Force.