Keep An Eye On Your Path – Coriolis Effect

Introduction of Coriolis Effect

In order to explain Coriolis force and its effect, let us start with an example that you would have seen in parks and playgrounds, the merry-go-round. All of us would have enjoyed it, but have you ever tried throwing something while on the ride. If you haven’t, then click the video below to watch it

 

 

In the above video, you can clearly see that the one who throws the ball is actually trying to pass it to the one sitting opposite to them. But each time the ball is moving towards the one sitting adjacent to them. You can’t notice this effect when the merry go round is at rest. This effect is known as the Coriolis effect and the force which does this job is known as the Coriolis force.

Coriolis force

Coriolis Effect
Source: Wikipedia Here are two different views of the same disc. The first disc shows the view from a non rotating frame i.e. when you view the disc from above. The second disc shows the view from a rotating frame i.e when you are standing in the red dot which is a part of the rotating disc

The Coriolis force is a force that seems to act on an object moving in a rotating frame. This force is a fictitious force which implies that it is not an actual force but created due to the difference in frame of reference as the absence of this force would create a conflict in the application of Newton’s laws.

Ball over a disc

Imagine a disc rotating in the anticlockwise direction having a ball at its center. Let that red dot be the position on which you stand. When the ball is undisturbed during the rotation, it will try its level best to stay in the same center. But when someone knocks it out smoothly towards your direction (i.e.towards the red dot), the ball starts to roll on the disc.

In this situation, if you are standing on the red dot which is a part of the rotating disc, you’ll observe the path of the ball being curved towards its right side. But when you view it from above (i.e.from an inertial frame) you’ll find that the ball moves in a straight line as it has to be.

You may find this weird. What actually happens here is that the ball is intended to move towards you when someone first knocks it out but this is just an opinion from your moving frame of reference. The ball, when viewed from above has to move towards a fixed point in space which was the initial position of the dot at the moment the ball was knocked. So the ball is actually moving towards a fixed point in space whereas it is the position of the red dot which is changing continuously.

As a result, you’ll observe this curved path of the ball which was supposed to move towards you straight. Here from the perspective of red dot,  it looks like some force is acting on the rolling ball thus moving it away from the dot in a curved path. This is also the reason why you experience a curved path in merry go round.

These types of forces come under the category of pseudo forces and as the one we deal with here is due to a rotating frame we call it Coriolis force.

Pseudo force

In case you aren’t still clear about a fictitious force (or pseudo force), consider you are standing in a lift halted at the 30th floor of the building. You have a book that is hooked to the weighing scale in your hand. The scale shows the mass of the book as 900 gram. Suddenly the rope of the lift is cut down and the lift you are standing in starts to fall freely without anything to stop it except the ground which you are about to hit within seconds.

So you know that you are about to sacrifice your life for the mere sake of understanding this article (applause from our GoPhysics Team). But you haven’t finished your purpose yet, so you now have a look at the weighing scale as a determined researcher. The scale won’t show any mass (i.e.it shows 0 kg).

But why???

The reason why the scale shows 0 kg may baffle you in the midst of a disaster. In the initial case when you are in a halted lift, the book you are holding experiences an acceleration downwards due to gravity whereas the scale you hold is the object which experiences the force given by the book which is accelerating and that is why the scale is capable of measuring the book’s weight.

But in the 2nd case when the lift is falling freely, along with the lift everything contained in it (scale, book and the great you) falls at a rate of 9.8 m/s^2. In this scenario, as you are in the lift, nothing seems strange except the scale you held in your hand showing no weight.

This confusion can be cleared when you are someone looking from outside. From this perspective, you’ll find that everything including the lift falls at the same rate and that is the maximum possible acceleration at which gravity can pull you. So the hook of the scale you’ve held is just in contact with the book and the book does not exert any force as the scale is also falling with it and there is nothing to pull the scale back. This results in the weightlessness of everything inside the lift.

When you view all this from outside, you’ll know that everything is falling at the same rate and it is impossible for something to exert a force on another. Here the perspective of the person standing in the lift is known as a non-inertial frame and the perspective of one who’s viewing the whole event from outside is known as an inertial frame. Such events have to be viewed from the inertial frame in order to make sense.

How it affects us

Let’s get back to Coriolis force and how it has an impact in our living world. Suppose you are in Uganda which is at the equator and your friend is in Finland which is somewhat closer to the poles. You throw a ball straight to your friend standing in Finland (which we know isn’t possible but let us assume yourself having something like a hulk gene). Your friend has to wait there for his eternity to get your ball because the ball has been diverted towards the right and fell somewhere in Russia.

coriolis effect
Orange arrow shows the resultant path while the yellow represents intended one

Differential speed of the earth

What you saw in the above example is due to the Coriolis effect that we experience due to earth’s rotation. Our planet takes about 24 hrs (actually 23:56:04 hrs) to complete a rotation and as a whole, it has an angular velocity ≈7.29 × 10−5 radians/second. But it is just the angular velocity that remains the same throughout the planet when you speak about the linear velocity it varies with latitude.

Our earth has a varying linear speed (tangential) due to its spherical shape (Geoid actually). Keeping two poles as the axis, circumference of the earth is larger at the equator whereas the region near the poles has a smaller circumference.

The circumference at the equator (0º latitude) is about 40,075 km, so it has to move at a speed of ≈1700 km/h to complete a rotation in 24 hrs which is the linear velocity of that portion of the earth. If we take the latitude at which your friend stands as 61.92ºN latitude, circumference is about 24,540 km. At this latitude, the earth has to rotate at a rate of nearly 800 km/h. This linear velocity of the planet decreases with an increase in latitude, in both the north and south direction.

Any planet with a shape like the earth has to exhibit this difference in linear velocity with respect to its axis in order to prevent the planet from collapsing.

coriolis effect
Difference in linear velocities of different latitudes (approx.) which is equidistant from equator

Coming back to ‘Ball and the eternal friend’ problem

In the problem we dealt with, when you are standing in Uganda, you are moving at a velocity of 1700 km/h (towards east) along with the earth and your friend in Finland moves at about 800 km/h(towards east). Along with you, the ball has the same velocity of 1700 km/h east. So when you throw the ball in some direction, in addition to the velocity imparted by you, it’ll posses that 1700 km/h(east) with it. Thus,

Final velocity of ball = Velocity imparted by your action + Velocity imparted by the earth

The ball you threw, on its way to your friend, will have this resultant velocity and so it moves in that direction. The portion of the earth in which your friend is standing should also move at the same 1700 km/h(east) to get the ball straight into your friend’s hand in Finland despite the resultant path it is trying to seek. But your friend in Finland has only a linear velocity of about 800 km/h(east).

This difference in velocity between its point of projection and point of contact makes the ball move away from the path planned by the projector(i.e.you). As a result, the ball moves towards its right due to the velocity it got from the equator and falls in Russia which is in the east to Finland. This is how the Coriolis force acts in rotating spheres.

Note: The description of Russia being used here is just for giving you an understanding of the Coriolis effect. It doesn’t necessarily have to fall in Russia and could be anywhere else depending upon the velocity of the projectile.

An airplane departed from Uganda also experiences the same. In the olden days, airplanes had to regularly check their path in order prevent the Coriolis force from changing its path. The invention of GPS has changed this and made tracking the route easier.

Shaping the Hurricane

coriolis effect
Wind flowing from high to low

In our atmosphere, winds always move from a high-pressure area to a low-pressure area. But do you know that even these winds experience the Coriolis force which decides their rotation?

coriolis effect
Coriolis effect affecting the hurricane spin

Consider the Northern hemisphere in which wind from a high-pressure region, say Andaman islands moving to Delhi, a low-pressure region.

When we say they are moving from one place to another, the very first scene that comes to your mind would be their movement in a straight path. But it is not, during their flow they try to make a straight path but Coriolis force prevents it from happening so and bends them to their right.

Thus it takes a curved path which is bent near Delhi. Despite the deviation it experienced from Coriolis force, it is still attracted towards the low pressure region (Delhi). This makes it again take a curve and the air from high-pressure region flows like a spiral to Delhi. As they have deviated towards their right despite the direction of their origin, they always experience an attractive force from their left due to low-pressure regions.

Thus the spin of these hurricanes will be an anti-clockwise direction in the northern hemisphere.

 

coriolis effect
Hurricane spin differing with hemispheres

 

In the southern hemisphere, it is similar to the one we explained above but here the Coriolis force acts towards left. Thus making a path bent towards the left. Here when they experience a low-pressure pull, they’ll be attracted towards their right which will end up in a clockwise spin.

This Coriolis effect won’t just stop with these examples. This happens even in your sinks and toilet flush. Water spins clockwise in southern hemispherical countries like Chile, Australia, etc,… and anticlockwise in India, Canada, etc,.. But this effect is often countered by turbulence created by their structure,air, and other factors.

DO YOU KNOW that Coriolis effect also has a role in creating the earth’s  magnetic field? Check our article here.

Discussions are welcome in the comments!!!!

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