Hold on here … I’m not the brightest bean in the taco … but even I know that fake forces can never ascribe natural phenomena. The Coriolis force doesn’t exist as an actual force. My dog-earred copy of Halliday/Resnick makes NO mention of Coriolis force and very very little of the other famous pseudo force, centrifugal force.
I’ve waded into this controversy far enough to see that the Coriolis effect as The Master uses it is caused by the actual and real Pressure Gradient Force and not the imaginary and magical Coriolis force. It’s just not scientific to say hurricanes are initiated by magic.
“You try explaining convection currents and the Coriolis effect in 600 words or less.”
C’mon, we’re the teeming millions, we can do this … well, teeming hundreds … maybe teeming tens … grr, there has to be at least one or two Fluid Mechanics out there. I can’t find the straight dope on this anywhere on the web, because it belongs HERE. We can do this, and after 40 years of The Master busting his guts to make us laugh, it’s high time we returned the favor. Just how hard can it be to describe La Grange derivatives to people who failed high school Algebra four straight years, in 600* words or less?
= We all know snarky liberal/hippy/Commie McGoverniks proofreaders can’t count past 10 without taking their shoes off … so we can lie about number of words … (shhh, don’t tell anyone)
The coriolis force is inertia in a highly specific context. A fluid (the atmosphere) is subject to inertia as the solid earth rotates beneath it, partly pulling the atmosphere along but not without some shear effects.
Sigh… This whole label of “fictitious force” is an unfortunate accident of history, like “imaginary numbers” (which are just as valid and “real” as the “real numbers”). An ordinary force is exerted by something. A “fictitious” force isn’t exerted by something, but rather is a result of the frame of reference one is using. It’s still just fine to use them in calculations, though, and the Coriolis and centrifugal forces are exactly as “real” as gravity (another force which is purely the result of the reference frame one chooses).
My frame of reference is stationary with respect to the stars watching the Earth spin underneath me. I cannot observe the Coriolis force, only infer that a person standing at 45º latitude can. Correct me if I’m wrong, but I can apply Newton’s Laws of Motion directly and get correct results … whereas our cannoneer standing at 45º latitude would get incorrect results if he applied Newton’s Law directly.
Frame of reference is central to this question, and a major source of confusion. I can’t imagine explaining it in 600 words or less.
I have Halliday/Resnick’s “Revised Printing”, 1974, p. 83:
I haven’t gone word-by-word, but I think the rest of the book uses the term “gravity”. I think I just gave a clue on how long ago I actually studied this. Most is a bit fuzzy, except a vivid memory of my instructor saying in no uncertain terms that the Coriolis force has nothing to do with [meteorology].
watchwolf49, you’re the first person in this thread to mention centripetal force. The OP was asking about centrifugal force, a related but different concept.
Both of you can apply Newton’s Laws directly and get correct results, provided that you each include all relevant forces in your calculations. For the person standing on the ground, those relevant forces will include the centrifugal force and the Coriolis force. Depending on the situation, the calculations may be for easier for one of you or for the other. If both methods give correct results, then it only makes sense to use whichever method is easier. That will often be the method in the rotating frame with the “fictitious” forces.
Seems fairly simple to me: when asking why the wind blows from west to east we are implicitly describing what happens in the Earth-centred rotating frame. It is hardly inappropriate then to describe the physics in terms of the ECRF and in particular the pseudo-forces that exist in that frame.
If we describe in terms of the Earth-centred inertial frame, then our description becomes different. We are asking why does the atmosphere rotate slower than the Earth’s surface (or a slightly more nuanced question).
We don’t need to invoke pseudo-forces to describe the physics in the ECIF, but if we transfer to the ECRF then those pseudo-forces are bound to appear in our description of the physics and the view that there’s something wrong about invoking pseudo-forces is viewed as rather archaic these days.
Newton’s Second Law of Motion is expressed most simply from an inertial frame of reference (IFR), F=ma. The same can be said of the First Law of Thermodynamics and Newton’s Law of Gravity. The Equation of Motion for a Fluidis derived (PDF file) from these three and can be expressed, in an IFR:
dv/dt = B + G + F[sub]friction[/sub]
Where dv/dt is the total acceleration, B is due to the pressure gradient force, G is due to the force of gravity and F[sub]friction[/sub] are due to the frictional forces … note that bold face type means this is a vector quantity.
When we calculate the work done, we can simplify by noting that pseudo forces can do no work. We can say that
G = g + C[sub]r[/sub] + C[sub]f[/sub]
Where (and added to above) g = gravitation, C[sub]r[/sub] = Coriolis force, C[sub]f[/sub] = centrifugal force
Substituting and setting C[sub]r[/sub] and C[sub]f[/sub] to zero we have
dv/dt = B + g + F[sub]friction[/sub].
My stumbling block here is I don’t understand how just using a component of one term changes the frame of reference. All the other terms are expressed in an IFR and the results of the work calculations are true for an IFR.
My point is that the overwhelming causative agent here is gravity, specifically that component of gravity that is directed at, and is perpendicular to, the axis of rotation. Friction has a minimal impact in the large scale circulation pattern. Think of it this way, a parcel of air moving up in latitude retains it’s velocity, but the Earth below is slowing down. Someone standing at the higher latitude would perceive air motion from west to east. In the tropics and polar regions, the air flows to lower latitudes, the person standing at the lower latitude would perceive an east to west motion.
A pseudo force is something that isn’t really a force but from certain points of view it LOOKS like a force and for in certain situations it can actually help you predict the outcome of an experiment if you pretend that it’s a real force.
When you are in a bus traveling 100 kph and the bus follows a curve in the road to your left, the sandwich sitting in your lap might slide to the right, as if it were being acted upon by some invisible magical “centrifugal” force. The truth is that your sandwich is following a straight line because it has inertia and it’s your lap that is moving to the left. There is is no such force acting on the sandwich. (There actually are two equal and opposite forces here, one centrifugal and one centripetal, but the centripetal force is being exerted by your lap onto the sandwich and the centrifugal force is being exerted by the sandwich onto your lap. There is no centrifugal force being exerted on the sandwich by anything.) But when you’re sitting in the bus and you see a left turn coming up, you would be wise to hold on to your sandwich. The whole problem stems from your perception that the bus is an inertial frame of reference, which it isn’t.
Similarly, when you aim a cannon at a hilltop 5 km east, you may be disappointed to see the cannonball veer off to the south, but that’s an illusion based on your mistaken assumption that the ground beneath you is a stationary platform. The truth is that the Earth is rotating and the cannonball is in fact following a straight line (I’m talking about left-right here, not up-down. Yes I know it’s going up and then down.) while the hilltop you’re aiming at is NOT following a straight line. But for the purposes of aiming the cannon, you can make up tables which say just how much this magical force which acts on the cannonball making it veer to the south will affect the trajectory and how much you should adjust your aim accordingly and that will give you a close enough answer that you might actually hit your target.
On a macro scale, the Coriolis effect results in shifting wind patterns as the air masses try to move in a straight line and the ground beneath them curves away in a slightly different direction. There is no “force” but the effect is real.
Nitpick: Hippie is spelled with an -i-e, like cookie.
And it’s expressed in exactly the same way in a non-inertial frame; you just need to include the “fictitious” forces in that F. The only issue with using Newton’s laws in a non-inertial frame is in the third law, not the second, and even there it’s not broken, it’s just not relevant for the “fictitious” forces.
OK, so you do accept the validity of fictitious forces, then. If you’re accepting and using gravity, then why not Coriolis? Both are simply products of the frame of reference, and disappear in an inertial frame.
I don’t think I’ve ever heard this explained so well. The statement is short, clear and completely accurate. How good is it? Substitute the word “science” for “force” and the whole statement is STILL completely true. This cuts straight to the heart of what pseudo means.
The air mass is moving south to north in the northern temperate zone, at the surface; north to south at the tropopause. Here’s a diagram from Wikipedia showing the heat convection cells as we observe them in our atmosphere. The question here is why there is a west to east component, at the surface, in addition to the south to north component (and this is an east to west component at the tropopause). As you said, the Coriolis force only LOOKS like a force. However the wind just doesn’t look like it’s blow from the west, it really is blowing from the west. The air parcel contains kinetic energy that moves it along this axis. Pseudo forces never transfer energy, therefore there must be some other force driving the Westerlies.
Think of it this way, if we’re interested in the motion of the cannonball, why should we can about the motion of the cannon after the ball has left? The change in kinetic energy of the cannonball has absolutely nothing to do with the change in kinetic energy of the cannoneer after the ball has left the cannon.
I specified in the OP that I want to use Newton’s 2nd directly, as F = ma. I understand we can also use F[sub]x[/sub] + F[sub]y[/sub] = m ( a[sub]x[/sub] + a[sub]y[/sub] ), but that is not simpler. The simplifications comes after we’ve evaluated the forces involved, when we evaluate for work done. Coriolis force is a pseudo force, thus both pseudo forces do NO work and can be safely removed from our equation of motion. This leaves the gravitational force (as defined in my previous post) as the only force that causes the Westerlies. This is what gives the air parcel it’s kinetic energy along the west-east axis and thus completely describes it’s motion along this axis.
Yes, I accept the validity of ignoring fictitious forces, they cannot transfer energy. You’re last sentence has me completely confused. Yes, the Coriolis force disappears in an inertial frame of reference, but gravity sure doesn’t, not in the Newtonian universe.
The Coriolis effect is caused by the gravitational force, and has nothing to do with the Coriolis force except in it’s absence. This is in the meteorological context, which is proper for The Master’s article.
Who said anything about x and y components? No matter what reference frame you’re in, F = ma works only if F means the sum of all forces. If you’re in an inertial reference frame, this might mean normal force from the ground, friction, air resistance, buoyancy, etc. If you’re in a non-inertial reference frame, it means all of those plus “fictitious” forces like gravity and the Coriolis force. You can express those forces using any coordinates you like, or even not using coordinates at all, but you still have to include all of them.
What Newtonian universe are you talking about? The one we live in sure isn’t.
This is an inertial frame of reference, and it is stipulated from the beginning. Do you disagree with the stipulation? Is it invalid? You agreed above that I will achieve correct results in this frame of reference. Are the results I gave in this inertial frame of reference somehow incorrect?
The Newtonian universe is one for which the passage of time is absolute, it doesn’t matter your velocity. You and I live in a universe where the passage of time is relative, it depends on our velocity. However, we can safely ignore the fact that the air mass experiences the passage of time at a different rate than the anemometer does … 11.2 mph is close enough.
“Classical Physics” is probably the more proper term.
I must remember to call this forcibly to gravity’s attention the next time I fall off a tall building. “You are purely the result of a reference frame which I now choose not to use. Now go away and quit making me drop like a stone.”
Sorry, Chronos, I’m not quibbling, I realize you know this stuff like the back of your hand. It’s just kinda weird that a ‘fictitious’ force could introduce you to the sidewalk with such abrupt intimacy.
How is that any weirder than flying off a centrifuge into a wall? Fictitious forces result in real-world consequences when Newtonian paths intersect.
General Relativity is a little weirder in that paths that start off parallel can eventually intersect, but that’s a function of the weirdness of curved space, not pseudoforces.
Really, honestly? That’s like saying astronomy has no scientific basis because of astrology. Is relativity cod-Riemannian geometry because it uses pseudo-Riemannian manifolds rather than Riemannian manifolds?
Well actually the free-falling frame of dropping off a building is exactly the frame that makes “gravity go away”. As Douglas Adams said: it’s not the fall that kills you, it’s the sudden stop at the end.
