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The Coriolis force and the conservation of angular momentum

The Coriolis force and the conservation of momentum are responsible for some the larger-scale features of ocean circulation.
MARK BRANDON: When you’re an oceanographer, one of the great tricks you can use is children’s playgrounds to demonstrate some of the most important principles. And the principle I’m going to demonstrate at the moment is the conservation of angular momentum. And I have to say, this is my idea of hell. I hate roundabouts, but we’re going to give a go.
And you can see it’s speeding up. And if I go out, it slows down. And if I go in again, it speeds up. And I think that’s the end of me for today.
So the next thing I’m going to demonstrate is the Coriolis force. Now the Coriolis force is a fictional force that we use to compensate for the fact that the earth is rotating. Now we know the earth rotates once every 24 hours. That’s where we get night and day. What I’m going to do is use this ball on this roundabout behind me. Because the earth is rotating, things moving on the earth get deflected. Now in the Northern Hemisphere, things get directed in one direction. And in the Southern Hemisphere, they get directed in the opposite direction. Let’s try it and see what happens.
As you can see, the ball’s path is deflected because of the rotation of the roundabout. When the roundabout is stationary however, the ball travels in a straight line.

In this step, Professor Mark Brandon demonstrates two key processes responsible for creating ocean gyres.

Angular momentum

The first process demonstrated in the video is something you may be familiar with as it is something you could have experienced: the conservation of angular momentum. At first the roundabout spins rapidly but the rotation is slowing through friction. As Mark moves his body further from the axis of rotation then the rotation slows even more. However when he move closer to the centre of the rotation axis, the roundabout noticeably speeds up even though friction is generally slowing the roundabout down.

What is happening is that the energy is being conserved. If we ignore friction, then the further Mark is from the axis, then the slower the rotation, the closer to the axis the more rapid the rotation. This is simply an example of the conservation of energy and in this case it is called the conservation of vorticity. It is fundamental to understanding the ocean currents.

To clarify this further, let’s think of momentum as mass times the speed at which it is moving. Let’s imagine Mark’s roundabout is rotating at a rate of one full turn per 5 seconds and let’s say the circumference (distance) around the outer edge of the roundabout is 5 metres. So when standing on the outer edge, in one full turn of the roundabout, Mark travels 5 metres in 5 seconds (i.e. his speed is 1 metre per second). So his momentum will be his mass times 1 metre per second.

But when Mark moves in to the centre of the roundabout, he is now travelling a shorter distance (around a smaller circle) during each turn of the roundabout. Let’s say that the circumference where Mark stands near the centre of the roundabout is 2.5 metres.

If the rate of the roundabout’s rotation stayed the same, Mark would now only travel 2.5 metres in 5 seconds (i.e. 0.5 metres per second). So his momentum would be half what it was before (his mass has not changed). Instead, for his momentum to “be conserved”, i.e. remain constant, the rate of the roundabout’s turn must change – speeding up if he moves inwards, and slowing down if he moves outwards.

Angular momentum can also be observed when watching ice-skaters spin. As they bring their arms and legs in closer to their core, they spin faster. Opening their arms out slows them down.

The Coriolis Force

In the second part, we can see that when something is in motion on a rotating platform it is deflected by an apparent force we call the Coriolis Force. The same process happens on the rotating earth and the direction of deflection depends on the hemisphere one is in. In the northern hemisphere moving objects are deflected to the right, whereas in the southern hemisphere they are deflected to the left. The magnitude of this apparent Coriolis force which we use to account for the deflection is dependent on the distance from the equator (so latitude), and it is zero at the equator and increases towards the poles.

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Exploring Our Ocean

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