Hi, this is Module 12 of Three Dimensional Dynamics, and today's learning outcome is to use that theory we developed last time, and we're going to explain how Coriolis acceleration is related to the deflection of air rushing towards a low pressure area, and thereby forming a hurricane. And so, here's where we left off. Last time we had the earth as a moving frame. We said this was not to scale, but we had a particle close to the Earth. We came up with a differential equations of motion for that particle and this is what we arrived at at the end of the last module. Now I want to do a hurricane example. And so I want to explain in detail what happens when air rushes to low, low, a low pressure area. And so here's a, a video clip of an actual hurricane. In the in the northern hemisphere. And it is not happenstance which direction the hurricane rotates, it always rotates in the northern hemisphere the same, direction. And we're going to find out why that is so in this, in this module. And so, we're going to look at an alternate view from my theory. We're going to look at from the side, so we're looking straight on to the low pressure so we're going to rotate ninety degrees here. Let me, let me show you what I mean on my demo. So we develop the theory with our moving frame here. And so I'm just going to take an alternate view. I'm going to rotate it ninety degrees and now my Z axis is going out, my Y axis is up and my X axis in, is in this direction. So here, here is that view again. The Z axis would be coming out and so air is going to be flowing toward that low pressure center. And we're going to ignore the motion in the z, or z double dot, or z direction because z dot and z double dot, those are the velocities and accelerations towards the Earth. I just want to find what's going on in the horizontal plane. And so we're also going to ignore the external forces, because I'm going to look at a particle of air that's free streaming, free streaming towards that low pressure center. So, here again are the equations of motion we came up with. Let's first examine a little particle that's coming down the Y axis towards the low pressure center, so coming down in this direction. So here's our situation. We're going to say that that particle has a constant velocity, that's going to be the relative velocity with respect to my moving reference frame. It's going to be Y.J. and in this case, I'll just say it's just minus U sub P, where P is for the particle, so it's got some velocity in the negative J direction, and it's a constant velocity. And so, if I put that up in here I know Z dot was being ignored I said f.x was not there and so I end up with x double dot equals minus 2 omega U sub p sign of lambda. And so what, if I look at that particle with Newton's second law, F=MX double dot, the force associated now, with that Coriolis acceleration is going to tend to move that particle in the negative X direction. And so that means that a particle coming down here from the top is going to turn toward the, the left or the negative x direction. Okay. Now let's look at a particle coming in, in the positive x direction from the left here. And in this case, v rail is going to be x.i or again some constant velocity use of p in the i direction. I can put that in now, here, u p, and again, no external force. And so I end up with y double dot is a negative value, so f equals ma of y double dot is a negative value, that means the force associated with it will tend to move the particle in the negative y direction in this case, and so now I've got this particle coming in, going down in this direction, and I just keep on going now. Let's look at a particle moving, in the positive Y direction, so V rel equals U sub P in the J direction. Again I can substitute that in here, Z dot and this one go away, I get, now X double dot is a positive value. And so this particle is going to tend to have a force that's moving it in the positive x direction, like this. And then finally. [BLANK_AUDIO]. We'll look at the particle coming in from the right. It's V rel now is minus u sub p. Substitute that in x.u sub p here, this goes away, that's a negative and a negative here is going to make a positive, and so I get a positive term and a negative term, but I know that omega is very small, it's, it's a small number for the rotation of, the angular velocity of the earth and so if I square a very small number, omega squared. I can actually neglect, or this terms going to be a whole lot smaller than this term. So this is a positive value which means this force is going to be pushed in a positive Y direction. And so here's what I end up with for each of the directions coming in, and so what happens is these particles therefore swirl in a counter clockwise direction. And that's why hurricanes, as you saw in the video, rotate in a counter clockwise direction in the northern hemisphere. Now I know I have students from all over the world watching these this, this course. And so what I'd like for you to do on your own is try to predict what direction a storm like this would rotate in the southern hemisphere. And so as an exercise on your own, do the southern hemisphere, and as I say, really interesting example and we'll come back next time and continue the course.