No such thing. The principle of general covariance says that it doesn’t matter. In fact, there’s no such thing as an “accelerated” or “non-accelerated” frame. It’s just that the curvature effects of the coordinate change are noticible for cases where we classically describe a “centrifugal” force. The percieved centrifugal force is just a side effect of the local diffeomorphism applied.
I don’t think this works. ma is certainly force, but mv[sup]2[/sup]/2 is energy (force time distance).
I think that the concept of centrifugal force just serves to help introductory physics students get even more confused about circular motion.
People like Chronos and scr4 can easily shift their thinking from an inertial reference frame to a non-inertial reference frame, but in my experience, your average student just gets them confused.
I think that it’s best to consider only the inertial frame of reference, and keep centrifugal force out of the picture. (This is because, of course, centrifugal force does not exist in such a frame. And I’m not going anywhere near general relativity.)
By “forces always come in pairs,” Jinx, you are referring to Newton’s 3rd Law. What you have to realize, though, is that the pairs of forces act on different objects.
To consider your various examples:
-
For a planet in orbit, the force pair is the attractive force of gravity of the Sun on the planet; and the attractive force of gravity of the planet on the Sun. The former is equivalent to the centripetal force on the planet. Note that the planet is undergoing circular motion, therefore it is accelerating, therefore by F[sub]net[/sub] = ma, there is a net force being exerted on it (the planet). The planet is being kept in orbit by this force.
-
For a ball on a rope, the force pair is the tension of the rope pulling the object in toward the center; and the tension of the rope pulling outward on your hand. Note that this outward force on your hand is not acting on the swinging object.
-
When you are in a car going around a curve, the force exerted on you by the car door is forcing you to go in the direction of the turn. The reaction force is the force exerted by you on the car door. Note that you can only feel that a force is being exerted on you; you cannot feel the direction of a force. The fact of the matter is that you are being forced inwards, despite your perception.
-
Another example is clothes in a washer during the spin cycle. The clothes are not being forced outward. Instead, the walls of the washer are exerting an inward force on the clothes that causes them to move in a circular path.
The equation is properly:
F[sub]net[/sub] = ma = F[sub]centripetal[/sub] = mv[sup]2[/sup]/r,
where v is the tangential (linear) velocity, and r is the radius of the circle in which the object is moving.
Errr, I mispoke. My brain thought I was responding to one thing, when it wasn’t really that thing at all.
I think the best way to think this from a physics student’s POV (i.e., no law of equivalence, no general relativity), is to constain a universe to just two objects. A single fencepost kinda thing and a ball connected to it by a string. No gravity, no nothing. You pull the string taut, and send the ball flying.
Now the string is a carrier of force in a sense, so we’ll ignore the fact that the post is pulling on the string and the string is pulling on the ball and just say the post is pulling on the ball. So the post is pulling on the ball (centripetal force), but then there has be another second law force in there right? Well, the only other place force can come from is the ball pulling on the post. However, the post is more or less immobile, so it doesn’t move. That causes the ball to go around in the circle, only two forces, nothing called centrifugal force is needed.
Of course in this situation, the forces will not all cancel, which seems to bother some. But that should be the case because the ball is constantly accelerating.
[QUOTE=robby]
The equation is properly:
F[sub]net[/sub] = ma = F[sub]centripetal[/sub] = mv[sup]2[/sup]/r
[QUOTE]
Right - that works.
Yeah, sorry for the typo. Of course if the radius just happened to be 2…
From the physics faq
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#14
And of course no information is propagating faster than light, which is really what relativity is all about.
Very true. Perhaps it should never even be mentioned, but it is often the “easy explanation” offered in elementary schools.
Frames of reference are hard to picture. It was a great help that scr4, I believe, helped define what one’s perspective would be as seen from each frame of reference.
[quote]
…By “forces always come in pairs,” Jinx, you are referring to Newton’s 3rd Law. What you have to realize, though, is that the pairs of forces act on different objects. To consider your various examples:
- For a planet in orbit, the force pair is the attractive force of gravity of the Sun on the planet; and the attractive force of gravity of the planet on the Sun. The former is equivalent to the centripetal force on the planet. Note that the planet is undergoing circular motion, therefore it is accelerating, therefore by F[sub]net[/sub] = ma, there is a net force being exerted on it (the planet). The planet is being kept in orbit by this force.
[quote]
Although the above should seem so simple, I still do not see it so clearly. Yes, I’ve run through the calculations, but it is a subtle concept to see.
When someone says the sun tugs on the earth, and the earth tugs on the sun (mGM/R^2)…now, this very straight forward to me.
And, while I understand why the tug from the sun can be equated to the centripetal force, it is not as obvious. The tug from the sun, it and of itself alone, is not centripetal force - for the sun tugs on me, too, for example. But, rather a coincidence of circumstance must be present for the centripetal force to manifest itself.
I think my mental stigma is the way I was taught to picture things from way back. I shouldn’t just be thinking that gravity is pulling on a planet. Instead, I need to evaluate the whole superposition of circumstances to get the full picture. IOW, yes, gravity is pulling the planet inwards, but the planet has its own motion it would like to maintain (thank you very much) and its inertia will resist the inward pull hence combating the inward. Combining these two facts manifests the centripetal force. Well, at least it helps me to think of it like this now.
Your other examples I have an easier time understanding and picturing. Thanks for your help, Robby…I say, olde chap, very good post! - Jinx
It sounds like you are thinking of centripetal force as a consequence of rotation. It’s not. “Centripetal force” means “the force that is causing the object to move in a circular path.”
If there was no force acting on an object, it will travel through space in a straight line. If a force pulls or pushes it sideways momentarily, it will “accelerate”, i.e. its path will be bent, and its velocity will change. (Speed will be the same, but velocity is a vector, and the direction of the vector will change.) If you can arrange a system so that a foce pushes or pulls an object to the side continuously, the object will accelerate continuously to the side; that is, its path will continue to bend. In other words, the path will be a circle. The force that is, um, forcing the object to stay in this path is the centripetal force.
The problem with this is that students have actually experienced centrifugal force and are familiar with it. An introductory physics student might ask a question like “When the car turns quickly, why am I pulled towards the outside of the curve?”, but he’s not likely to ask “When the car turns quickly, why does the car door move in towards me?”. The question, as asked, is in the frame of reference fixed to the car, that is to say, the non-inertial frame, so it’s appropriate to answer it in the non-inertial frame.
And Jinx, you should not consider “inertia” as a force. Depending on what you mean by “inertia”, it’d be a mass or a momentum, neither of which even has the same units as force. When a planet is in orbit, you can’t say that inertia is opposing the gravitational pull from the Sun. The only meaningful way to assign a direction to inertia would be the momentum, and that’s at a right angle to the gravitational force, not opposing it. You can say that the gravitational force is opposed by a centrifugal force, and that the planet is therefore not accelerating. Alternately, you can say that there’s nothing opposing the gravitational force (which, in this case, is the centripetal force), and that the planet is therefore accelerating. Why doesn’t the planet fall? The answer is, it does. An object in orbit is always falling.
As for Newton’s laws not being valid in the rotating frame, they are, provided you introduce the fictitious forces, acting without a source. Which is, of course, why we introduce them in the first place.
Not really. Relativity is all about the principle of general covariance, which says that physics can’t depend on your reference frame at all. That no information propagates faster than light is a consequence of the hypothesis that spacetime is locally Lorentzian as well as the (philosophical) hypothesis of local causality.