Just spotted this. This is also incorrect: When you land, you will be moving straight down again, but you will have a net displacement backwards. Pushing something backward and then pushing it forward for the same amount of time will not result in its position going back to its original value; it’ll result in its velocity (in that direction, at least) going back to its original value.
If I remember my mechanics from last semester, the coriolis force is
-2 w x v
where w is the angular velocity and v is the tangential velocity. So, if we set the z axis right along the axis of rotation of the earth, then w is wo in the z direction, fixed with respect to the center of the earth. Now, if we consider a reference frame with the z axis pointing through the center of the earth, and the positive part pointing away from the center, the positive x axis is directly south, and the positive y axis is directly east. In this reference frame, w is pointing to the north(-x) with a component
wo cos(Lat)
and away from the surface(+z) with a component
wo sin(lat)
If we shoot a ball directly east, with a velocity vo in the surface frame of reference, then we have
{-wo cos(lat),0,wo sin(lat)} x {0,vo,0}
This results in a vector of
{-vo wo sin(lat), 0,-vo wo cos(lat)}
multiply by a -2 and we have a vector of
{2 vo wo sin(lat),0, 2 vo wo cos(lat)}
This is a force to the south and away from the center. So, it deflects to the right of its velocity vector and away from the earth. It depends on the latitude you are at. If you are at the equator, the force is only away from the earth for a projectile traveling east, because sin(0) is 0 and cos(0) is 1.
Yes, I already admitted that my example was bad and misleading. But I don´t think I really understand your point. Would you care to eleborate? And I´m really interested in it, no flame war intended.
Here’s a good link.
We’re talking about the coriolis effect on the water basin, or hurricanes? No vertical motion.
It’s a very small effect on the water basin, but still it vanishes at the equator, right?
Water flowing down a drain has a vertical motion (up-down), so there is a Coriolis acceleration over the water draining at the equator. This acceleration is directed westword, so it does not cause rotation.
Forget the math and think physically. Every motion in a rotating system needs an acceleration that is orthogonal to the sense of the movement.
Let’s get back to the rotating platform, that is easier to understand than a sphere.
If you move keeping your distance from the center (in a circle), your angular velocity is varying, so you need a centripetal acceleration to keep you in that circle.
If you move along a radius, you keep your angular velocity, but since your distance from the center is changing, the module of your tangential velocity changes, so you need an acceleration in the sense of the change. this acceleration is Coriolis’. Of course you will need also a change in your centripetal acceleration.
Getting back to the Earth surface. If you move at constant speed along a paralel, you must change your centripetal acceleration in respect to a standing object. But there is no reason why you should deflect southwards or northwards.
I hope this enlightens z1221z too.
Ok, let´s go back to the turntable. What I was trying to say a few posts earlier ist this: If you shoot a ball straight while sitting on the turntable, form your rotating POV it will appear to be deflected, totally regardless of the direction in which you shoot it. To an outside observer, it will seem to go straight, also regardless of the direction in wich you shoot it. This is why the coriolis force is sometimes called a “fictious force”, since from an non rotating POV there is no deflection.
Your example has nothing to do with the Coriolis effect! It is simply a relative movement. As you said, the ball will keep a constant velocity for an observer in an inertial frame. But when you shoot the ball it is no longer in contact with your turning platform, so there is no Coriolis force acting over it.
The Coriolis force has nothing of fictitious. It is a real force. An object under the effect of the Coriolis force will have it’s velocity changed relative to the inertial frame.
Suppose you have a trench following the radius of your platform and you roll a ball with constant speed along that trench. For you, the ball is moving away is a straight line, with constant speed. For the observer in the inertial frame it will move in a more complicated trajectory.
But more important, for the external observer you have a tangential velocity v[sub]1[/sub]=wR[sub]1[/sub], where w is your angular velocity and R[sub]1[/sub] is your distance from the axis of rotation. For the same observer, the ball has a tangencial velocity v = wR, where R is the varying distance from the axis. Since the velocity of the ball changes, it needs a ‘real’ force to do the job. This force is provided by the wall of your trench.
Now, dig a trench following a circle and roll the ball with constant speed along it. Of course, the module of the velocity is constant, but it’s direction changes, so you need a centripetal force, also provided by the wall of the trench. If the ball moves with speed v[sub]2[/sub] relative to you, it will have an angular velocity in your rotating frame w[sub]2[/sub] = v[sub]2[/sub] /R[sub]1[/sub] and in the inertial frame w[sub]3[/sub] = w + w[sub]2[/sub] . So, while your centripetal acceleration relative to the inertial frame is w[sup]2[/sup]/R[sub]1[/sub], the ball is submited to an acceleration (w + w[sub]2[/sub] )[sup]2[/sup]/R[sub]1[/sub].
Of course my example has to do with the coriolis force. “Simply” a relative movement? You can say that the coriolis force is “simply” relative movement regarding a rotating frame of reference, because that´s all it is.
It doesn´t have to be in contact with the turning platform.
Of course, if there is friction between the moving object and the turntable (like an atmosphere rotating with it, or if you shoot a hockey puck etc.) the path of the object on the turntable will vary with friction. But the coriolis force acting upon it is still the same.
I know that the term “fictious force” is controversial, so put it in quotes, and said some people called it fictious.
There is no controversy! The Coriolis force is a real one, so you have to physically apply it. By physically I mean either the object is in contact with the rotating platform or there is some field making the connection.
I suggest that you follow your own advice and check any elementary physics book. The one proposed by Chronos will do.
Let me get this straight–it’s real like the centrifugal force is real, right?
Incorrect. If the only “force” acting on an object is the Coriolis force, then, when viewed from an inertial reference frame, the object’s trajectory will be a straight line with constant speed. In the sense that any force is “fictitious”, the Coriolis force is.
It depends of what you call centrifugal force. If you attach a weight to one extremty of a wire, take the other extremity in your hand and rotate it. The weight will be maintained in it’s circular path by a centripetal force. But your hand will be subject to an equal and contrary force, that we could call centrifugal. And yes, it is very real! You can be injured by it.
In my example of a ball rolling in a radial trench on a rotating platform, the only force acting over the ball is Coriolis, provided by the wall of the trench. For an observer that moves with the platform it’s trajectory is a straight line. For an observer on an inertial frame, the trajectory is a spiral.
I don´t understand what you mean by “you have to physically apply it”. Are you confusing the coriolis force with the friction between a moving object and the rotating frame of reference? There has to be no connection whatsoever between the turntable and the ball you shoot. The ball you shoot from your turntable in space will to be deflected form your POV, and the deflection is caused by the coriolis force.
Well, I just did. The post by Mines Mystique explained it nicely. And I also admit that I was wrong when I said that the coriolis force is zero at the equator, which is not true in the general sense. But for objects moving only horizontally, it is zero at the equator.
I also want to point out that you like to post lots of equations, which, although they are not wrong, often miss the point of the discussion. But when someone like Mines Mystique showed you the math that IS relevant, you said “forget the math… think physically”. Hmmm.
Nope. The very real real force acting upon your ball in the trench is the friction between the ball and the trench. That force is provided by the rotation of the turntable. Note that in your example the ball rolling along the trench will change the angular velocity of the turntable.
It seems we are talking about two different phenomena and calling both Coriolis. What I understand by Coriolis effect is what I stated in my example, the ball rolling in a trench. And the force deflecting the ball is the wall of the trench and not the frction. In general the friction will not be enough to maintain the ball in a stright line in reference to the rotating observer. That’s why I postulated a trench.
In my example, the Coriolis force is a very real one and chances the velocity of the ball in an inertial frame, making it follow a spiral curve.
In your understanding the Coriolis effect arises when the ball follows a straight line in the inertial frame and a complicated curve for the rotating observer. For this observer it seems that a mysterious force is deflecting the ball. Since there is relatuve change of velocity, second Newton’s law states that a force must be involved. This force is the centripetal force acting on the observer. The ball is subject to no force, real or fictitious.
About your rant over my asking Mines to froget the equations, let me explain my point:
Equations are a means to quantize an observed phenomenon. If you don’t understand the phenomenon, equations are just a bunch of symbols. All the equations I posted were describing the point I had tried to intuitivelly explain. The ones Mines lacked the intuitive explanation, that is why I asked him to forget.
Actually, the force the string is putting on your hand is not the centrifugal force. It’s tension. Centrifugal force only shows up when you’re in the rotating coordinate system. An astronaut in a spinning space station, for instance, will observe that his feet seem to be pulled “down” to the floor. The force he is feeling is the centrifugal force, and it is not exerted by anything. This is what is meant by a “fictitious force”. Now, it often happens that an object will be at rest in an accelerating (non-inertial) reference frame. In that case, you need some other force to balance out the fictitious force. In the astronaut’s case, this is the normal force of the floor on his feet. It might also be a frictional force, or an electromagnetic force, or any sort of force you please. This force will happen to have the same magnitude as the fictitious force you’re counterbalancing, but it is not the same force. It’s a real force, exerted by something. In the case of centrifugal force, this is the force which is called centripetal in the inertial frame.
The Coriolis force is a fictitious force, like the centrifugal force, and is not exerted by anything. It may be the case that there is some real force countering the effects of the Coriolis force, and you could even give that force a name. But nobody has yet seen fit to do so, and in any event that balancing force is not itself the Coriolis force.