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#55
Jun3008, 01:28 PM

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A science fiction setting:
Two fiercely competitive species find an airless, spinning planet chock full of metals. Each builds an armed mining outpost, only to discover the other species has also found the planet. One species fires first, consistently missing their enemy. The commander asks the science officer whether the firing system models the Coriolis force. The science officer says it's not modeled and won't budge when told to incorporate it because "It's not a real force". The commanding officer finds another solution: Make the guns aim at where the enemy outpost will be when the missiles hit rather than where it is when the missiles are launched. The science officer agrees to this, but says that this will take some time. Meanwhile, the other species retaliate. They come from a rapidly spinning world and have the Coriolis force factored in. It doesn't matter to them that the force is not real; the effect is real. Their guns are deadly accurate. ======================================================== All of this debate on whether the centrifugal and Coriolis effects are "real" misses the mark. Hurricanes form because of the Coriolis effect, and gravity varies with latitude in part because of the centrifugal force. These very real effects are explainable without the aid of fictitious forces from the point of view of an inertial observer. Sometimes an inertial perspective happens to be extremely inconvenient. Atmospheric modeling is one such example. 


#56
Jun3008, 01:48 PM

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http://en.wikipedia.org/wiki/Reactive_centrifugal_force I for one prefer to use non rotational, non accelerating frame of references, and centrifugal force should have a meaning in a more common frame of reference. Getting back to that person that is twirling an object, what do you call the outwards and rotating force that person applies at the contact patch between his feet and the ground (either a platorm on a frictionless plane, or the earth)? 


#57
Jun3008, 02:01 PM

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#58
Jun3008, 02:39 PM

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So it appears to be that we agree that centrifugal is a fictitious or virtual force created to balance centripetal in a specific ref frame. I still take issue with those who say Coriolis is not a real force. My understanding is as follows.
If we regard earth as a ref frame and wish to fire a projectile from the equator northward, we must account for rotation of the earth. When the projectile is fired, it has the velocity eastward equal to that at the equator. As it traverses its path northward, it maintains its eastward linear velocity while the earth underneath maintains its eastward angular velocity. When the missile lands north of the equator, its eastward velocity is greater than the eastard *linear* velocity of that spot on earth north of the equator. Hence the missile lands *east* of its intended target spot had Coriolis not been accounted for. I've always regarded Coriolis as a "correction term" that must be computed to account for the above phenomenon. While the missile is airborn, of course there is no literal "Coriolis force" acting on it to accelerate it eastwardly. From the earth ref frame, if we treated the earth as stationary then the missile won't land where we thought it should have. What "knocked the missile off course?" We add the Coriolis term as a correcting factor. The Coriolis component is not an actual force acting on the airborn missile deviating its path. Rather it is a correction term accounting for the fact that a rotating ref frame cannot be equated to a stationary one. There is no literal Coriolis force actively influencing the missile trajectory, but rather it is a correction term accounting for the deviation AS IF THERE WAS a "real" Coriolis force. The force is not literal, but the missile's path deviation is absolutely real. Coriolis force is a virtual force mathematically defined to account for A VERY REAL NONFICTITIUOS path deviation. That's my understanding of the "Coriolis component" using my undergrad physics prof Dr. M terminology. Dr. M knew his stuff. In 3 decades of EE R & D, his teachings never once failed me. He was brilliant. Dr. M, wherever you are, "you da man!" 


#59
Jun3008, 02:48 PM

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cabraham,
That's exactly why it is a fictious force. It is manifested only to correct for the fact that your frame of reference is noninertial. In firing a projectile (such as a missile) over long distances over the Earth surface, the Coriolis force will play a significant role. This is the noninertial view. But if your launch center was from a point in space, you wouldn't have to worry about the Coriolis force; you'd just have to account for the fact that you are firing at a moving target (the Earth). This is the inertial view. 


#60
Jun3008, 03:35 PM

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There is an easy test of whether a force is real or fictitious: Can you build a black box to measure the force? Fictitious forces arise from the observer's perspective rather than from some real force that truly does act on the body. Can we measure the normal force? Sure. You step on a scale every morning. Can we measure tension? Sure. Can we measure a centrifugal force or Coriolis force: Nope. These are observerdependent. They aren't real. One such measuring device is an accelerometer. The Newtonian view of a perfect accelerometer is a device that measures all real forces except gravitation acting on some body. Why that "except gravitation" clause? The GR view is "A perfect accelerometer is a device that measures all real forces acting on some body, period. There is no reason to exclude gravity because gravity is not a real force." 


#61
Jun3008, 06:41 PM

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I'm just a little goldfish who tries to make threedimensional sense out of the twodimensional images I see projected onto the boundary of the bowliverse. oooh … I've just thought of a question … forces do work … 


#62
Jun3008, 08:20 PM

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So when are they going to change the name of a centrifuge to a centripuge?



#63
Jul108, 07:33 AM

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Still don't have time to respond like I want; on my out the door again. I am going to need a vacation to recover from my current vacation at my inlaws! 


#64
Jul108, 09:33 AM

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It seems counterintuitive to me, but I want to say yes. Consider a particle placed on a rotating disc. The centrifugal force on the particle is [tex]\vec{F}_{cent}=m\omega^2\vec{r}[/tex] where r is directed radially. So in a particle being pushed from a point near the axis towards the edge of the disc, work must be performed: [tex]W=\int \vec{F}_{cent} \bullet d\vec{r} [/tex] My problem with this is where does the work go in the inertial frame? Also, clearly the Coriolis force cannot do work: [tex]\vec{F}_{Cor}=2m \vec{\omega} \times \vec{\dot r}[/tex] where dr/dt is the velocity of the particle in the noninertial frame. So I find it an oddity that one fictious force may do work while another may not. 


#65
Jul108, 10:34 AM

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Consider the following example. In an inertial frame, a particle is subject to a (net) force. Suppose that when the force starts acting, the velocity of the the particle is [itex]c \hat{e_1}[/itex], and that the velocity of the particle when the force stops acting is [itex]c \hat{e_2}[/itex], where [itex]c[/itex] is a constant. Because the initial and final speeds are the same, there is no change in kinetic energy, and, by the workenergy theorem, no work done on the particle by the force. Now consider the same situation from the point of view of an inertial reference frame that moves with velocity [itex]c \hat{e_1}[/itex] with respect to the first inertial reference frame. In this frame, the initial velocity of the the particle is [itex]\vec{0}[/itex], and the final velocity of the particle is [itex]c \left( \hat{e_2}  \hat{e_1} \right)[/itex]. In this frame, the change in kinetic energy and work done is [itex]m c^2[/itex]. 


#66
Jul108, 12:30 PM

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Excellent! Thank you for the very clear explanation. Bravo, Prof. Jones.



#67
Jul108, 05:01 PM

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Work done is peformed on the hanging object, it's weight times the height the hanging object is raised. Work is also done on the rotating object by the person, equal to it's change in kinetic energy. 


#68
Jul108, 06:13 PM

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#69
Jul208, 07:27 AM

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I, however, would not call a Coriolis force a correction term, it's a term that appears in rotating reference frames, just as centrifugal force does. The path of a particle is real, but the shape of the path is very dependent on the coordinate system used. Coriolis force and centrifugal account for the shape of the path in a rotating (with respect to an inertial frame) reference frame. As D H and Doc Al (and possibly others) have said, it's crazy not do some problems in a rotating frame. When doing such problems, Coriolis force and centrifugal force are treated as real forces for which intuition developed doing more elementary Newton's second law problems can be used. But it should be kept in mind that these forces are just artifacts of a noninertial coordinate system. Consider accelerometers that consist of two main parts  a hollow sphere like a basketball inside of which is a slightly smaller sphere. Initially, the centres of the spheres coincide, so that there is a small, uniform gap between the spheres. During acceleration, the gap will be closed, and contact between the spheres will be made. An alarm that indicates acceleration motion will sound. For zero acceleration, no alarm will sound, and straight line motion in inertial frames is indicated. An accelerometer won't measure acceleration due to either Coriolis force or to centrifugal force. Also, if a freely falling accelerometer is small enough that tidal forces can be neglected, it will measure zero acceleration, since both spheres fall at the same rate. Acceleration due to gravity, just like acceleration due to Coriolis and centrifugal forces, is independent of mass. Can gravity, too, be considered to be an artifact of a coordinate system? No and yes. Centrifugal and Coriolis forces at all points in space, i.e., globally, can be transformed away by a single transformation from the rotating frame to an inertial frame. For this reason, these forces are called fictitious. No single transformation will transform gravity away globally, but gravity can be transformed away locally by moving to a freely falling frame. If we expand the term "fictitious force" to include to forces that can be transformed away locally, then gravity also is a fictitious force. Pursuing this line of thought leads to the concept of gravity as spacetime geometry. I repeated the points that D H and tinytim have made, using slightly different words. As Doc Al has said, in mechanics courses, gravity is treated as a real force; it would be crazy to do otherwise. Considering gravity to be due to spacetime geometry, however, expresses something deeper about the physical world. 


#70
Jul208, 08:30 AM

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Let's take Coriolis. If we were to assume that the earth is NOT rotating, i.e. a stationary ref frame, while it actually IS rotating, what are the consequences? We err by not accounting for the rotation. So, we introduce a correction term in the kinetics/kinematics equations to account for this. But by doing so we are acknowledging the existence of rotation and an accelerated frame of ref. We say that we refer to earth as a frame of ref, but we do so with a priori knowledge that it is rotating. Thus we include the Coriolis term, twice the cross product of omega and u, to account for the rotation. I guess one could look at it your way, that the Coriolis force is "there" in the rotating ref frame. When a projectile is launched near the equator, in a direction away from the equator, the rotation of the earth gives the missile a large eastward component of velocity. The eastward component of points on the earth further from the equator is less. I'm speaking of linear velocity, not rotational, i.e. u = r* omega. In flight, the missile moves north (or south) away from the equator, while maintaining its eastward velocity imparted via earth rotation. When the missile lands, it has outdistanced its *intended* landing spot wrt eastward velocity. Hence it lands east of the spot expected if earth rotation was neglected. I guess you could view it that way, but it can also be viewed as a correction term. With respect to the earth ref frame, a "virtual" force knocked the missile of course in the eastward direction. The Coriolis term is intuitive and logical. There seems to be unanimous agreement that there is no actual "Coriolis force" knocking the missile eastward, i.e. Coriolis is "virtual". But in the course of the missile flight, where does "centrifugal" come into play? No one seems to produce the origin of this force, but are too quick to defend its significance. Also, no one has yet explained the origin of cf in the moon orbit question I raised earlier. Is anybody going to attampt to tackle that one? BR. Claude 


#71
Jul208, 08:53 AM

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Centrifugal force comes in as part of g. It depends only on position, just like gravitational force, and so it's just part of what we measure as g (which isn't exactly "vertical" anyway, because of mountains etc). 


#72
Jul208, 09:06 AM

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When we say that coriolis and centrifugal forces are artifacts of using a noninertial, rotating frame that does not mean that new physical effects magically appear when using a rotating frame of reference. The physical effects exist even in an inertial framethey are just much harder to analyze! (In an inertial frame, the effects are "simply" due to the fact that while a projectile goes "straight", the earth rotates.) If you do your analysis from an inertial frame, there is no need to introduce "forces" such as centrifugal or coriolis. (But good luck carrying out that analysis!) 


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