Why a Ball remains stationary

  • #1

Main Question or Discussion Point

Why a ball remains staionary when placed on a perfectly level surface?

It is because of an objects natural state is to remain "at rest" and due to friction? Also due to no forces acting on it on left or right side (-x, x) direction? What equation would one use to prove this?
 

Answers and Replies

  • #2
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This is just Newton's laws at work.

In the vertical direction, there are in an ideal situation only two forces: the force of gravity pulling the ball down on to the table, and the normal force that the table exerts on the ball to keep it from falling through. These forces cancel exactly, so there is no net force in the vertical direction. Since F = ma, this implies that a = 0, and the ball does not accelerate. Since it was not moving at all in the first place, it will never start moving (provided the forces stay the same).

In the horizontal direction, there are no forces at all (in an ideal situation), so again a = 0, which implies that the ball does not move.


Note that if the ball was already moving, then a = 0 does not imply v = 0. It then means that the ball does not accelerate, so it does not speed up or slow down. Simply because the speed v was already 0, it will stay 0 in your 'resting ball' example.
 
  • #3
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From Newton 'an object at rest remains at rest, or an object in motion remains in motion unless acted upon by an external force'.

'at rest' isn't a preferred state though. Newton's theories removed a preferred state of motion from the picture (as it ruins the idea of relative space) and such a ball would only be 'at rest' from your frame of reference because you are experiencing the same other motions as it (the earth spinning around it's axis, the earth orbiting the sun, the sun orbiting the milky way, etc, etc, etc) so it couldn't possibly be 'at rest', all it can be is stationary relative to you as an observer.
 
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  • #4
Why a ball remains staionary when placed on a perfectly level surface?
You're asking a "why" question.

The answer is the law of inertia. Enshrined as Newton's first law, but known by others before him, such as Galileo and Alhazen. If you are content with the following answer to your question, "because of the law of inertia," then that's one thing.

But if you're asking why is the law of inertia true, then that's another matter entirely. Nobel laureate Richard Feynman relates a story from his youth about asking his father why the ball in his wagon didn't move right away when he pulled the wagon. His father told him that nobody knows why the world is that way. Feynman as an adult admired his dad for having such a deep insight.
 
  • #5
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But if you're asking why is the law of inertia true, then that's another matter entirely. Nobel laureate Richard Feynman relates a story from his youth about asking his father why the ball in his wagon didn't move right away when he pulled the wagon. His father told him that nobody knows why the world is that way. Feynman as an adult admired his dad for having such a deep insight.
I saw that in a documentary about Feynman and it resonated with me, too. Life is a mystery.
 
  • #6
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When net forces actig at body zero or no forces is acting on it , the body will have no acceleraton that means the body continues the state of the motion , here the ball was at rest before so it will continue it being at rest.If the body was at the certain velocity it will continue with that.(Neglecting the friction, if there is friction certain force is neeeded to continue it in its uniform velocity) here you told that at left and right direction there should be no force acting ,but its not, it might be also that the equal force may be acting at body at left and right direction and therefore it might have nullified the net effect .(Note that there is the gravitational force acting at ball which is cancelled by reactive force of the surface)
here F=m(dv/dt)
if net F=0
o/m=dv/dt
dv/dt=0, velocity remains constant
since ball was at rest it continues the state v=0
 
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  • #7
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You're asking a "why" question.

The answer is the law of inertia. Enshrined as Newton's first law, but known by others before him, such as Galileo and Alhazen. If you are content with the following answer to your question, "because of the law of inertia," then that's one thing.

But if you're asking why is the law of inertia true, then that's another matter entirely. Nobel laureate Richard Feynman relates a story from his youth about asking his father why the ball in his wagon didn't move right away when he pulled the wagon. His father told him that nobody knows why the world is that way. Feynman as an adult admired his dad for having such a deep insight.

*raises hand* I'd like to ask a "why" question too if I may . . . um, I don't mean to ask why the law of inertia is true, but I do wonder how we know when it's going to work . . . that is, when it is applicable *tries to explain* I mean, we apply Newton's second law very happily to solids and fluids in inertial reference frames, but when we have to describe the motion in a non-inertial frame, we have to consider "ficticious forces" acting upon the solid/fluid particles, eg. if the reference frame has an angular velocity, then we have Coriolis forces to consider and such. Now, the Earth is rotating on its axis, so it's a non-inertial reference frame, ye? And okay, when we're using Newton's law to model the dynamics of a snowball rolling down a hill or a tumbling toast (gah, the examples - I know:P), then the Coriolis and centrifugal forces would probably be negligible and thus we consider the Earth an inertial reference frame for small scale applications . . . but on the other hand, to model weather systems, these forces would be important!

But! how do we know when a reference frame is inertial or not (and if we don't know, then why are Newton's Laws still valid in that frame)? I mean, the Earth is rotating around its axis and revolving around the Sun, but apart from that, maybe the whole solar system is accelerating with a ginormous acceleration . . . or if that's not true, then the whole galaxy, or the entire cluster of galaxies are aware of, maybe we're all just rotating at a lightning speed with respect to another cluster . . . so how can we define what an inertial reference frame is, and why are Newton's laws valid in a 'fixed' frame here on Earth? Maybe Newton's laws are not valid in the universe in general and rather they only are here on Earth because of the way the Earth is accelerating in the universe, that is, only in the Earth's non-inertial reference frame . . after all Newton developed it to work over here:P Is thus any reference frame that is accelerating differently to how the Earth is accelerating in the universe a non-inertial reference frame, in which you can't thus directly apply Newton's laws?

Um, maybe I'm not making sense and am missing something obvious:S but I just can't help wondering, and you guys are here to help me :)
 
  • #8
diazona
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First things first: to know whether a reference frame is inertial or not, you just measure it ;-) You can measure acceleration using an accelerometer. A simple example is hanging a ball on a string from the rearview mirror of your car; you can tell whether the car is accelerating or not by looking at the angle of the string. If it's hanging straight down, the car is not accelerating and is in an inertial reference frame. If it's tilted, the car is in a non-inertial reference frame. It's a fictitious force that makes the string tilt. If the force is large enough, you'll feel it too (like when you go around a tight turn and get pushed to the outer edge of the car, that's the fictitious centrifugal force at work).

Since we can measure accelerations, if the solar system were accelerating or rotating at a high speed, we'd be able to feel it, or at least measure it. And in fact we can measure the centrifugal acceleration caused by the rotation of the Earth. It's much smaller than gravity. The fictitious forces arising from the Earth's motion around the sun, around the center of the galaxy, etc. are smaller still. So while the Earth is technically not an inertial frame, for most purposes it's pretty darn close.

And as for how we know Newton's law apply to the rest of the universe: technically we don't, but we can watch the motion of distant stars and galaxies to see if there are any weird effects that show that Newton's laws are false. And there are some odd things that have been observed, but we explain them away by postulating dark matter (basically the idea that there's more mass in galaxies than you'd think by counting the visible stars) and dark energy (makes space expand, sort of explained by general relativity). I'm pretty sure some people have suggested that these effects are due to Newton's laws not applying in the distant universe, but those theories aren't particularly successful; it makes much more sense, and works just as well (or better), to use the dark matter/dark energy explanation. Believe me, if anyone finds solid, irrefutable evidence that the law of inertia doesn't actually hold, you'll hear about it ;-)
 
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BobbyBear said:
But! how do we know when a reference frame is inertial or not (and if we don't know, then why are Newton's Laws still valid in that frame)?
That's a good question. One in which I've been thinking about myself. In my opinion, no inertial frame is perfect. For example, you could choose the center of mass of all the objects in your frame and claim that as your inertial reference. But what if that frame is accelerating toward a massive object which you are not aware of. The affect of the massive object on your frame may be so small that it's not noticed. But as the frame draws closer to the massive object, or you take more accurate measurements, you may begin to notice that the objects in your frame are no longer obeying Newtons laws. So you then realize that your reference frame is not inertial after all. I wonder if this very thing could be happening with our own solar system right now? http://en.wikipedia.org/wiki/Pioneer_anomaly
diazona said:
to know whether a reference frame is inertial or not, you just measure it ;-) You can measure acceleration using an accelerometer.
But the accelerometer will not work if it's accelerating (free-falling) due to gravity.
 
  • #10
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But the accelerometer will not work if it's accelerating (free-falling) due to gravity.
This is why the "Vomit Comet" is used to train astronauts for free fall conditions. Free fall is a great inertial frame, but only inasmuch as the frame doesn't last long enough for the force differential to be noticeable between objects closer to the center of gravity versus objects further away. Most "inertial" frames have some type of limit on them, either time or position.
 
  • #11
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If we write down the potential energy P(x,y) of the ball resting on the table as a function of its coordinates x,y, and the derivative of that potential energy with respect to those coordinates is zero, then there is no force along those coordinates:

dP(x,y)/dx = 0 = Fx


dP(x,y)/dy = 0 = Fy
 
  • #12
But! how do we know when a reference frame is inertial or not
First things first: to know whether a reference frame is inertial or not, you just measure it ;-) You can measure acceleration using an accelerometer.
That's exactly right. Sometimes, though, you don't have the luxury of having an accelerometer traveling at constant velocity with respect to the inertial reference frame. More generally, any system of particles has an inertial frame. (This is what Newton's first law means.) However, the system is not obliged to have any particles in it traveling at constant velocity.

Consider two stars orbiting each other, for example. The system does have a coordinate system that's inertial (it actually has many), but neither star is motionless in that system.

In principle, the way you tell whether a coordinate system is inertial is by Newton's third law. If you're in an inertial reference frame, then a particle can only be accelerating because of a force. Any by the 3rd law, there must be some other particle in the universe that's experiencing the equal and opposite force.

So, if you pick a candidate inertial reference frame, look for particles that are accelerating. If each acceleration can be explained by the corresponding accelerations of other particles, then your frame really is inertial. If you have unexplained accelerations, then your candidate frame is not inertial.
 
  • #13
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His father told him that nobody knows why the world is that way. Feynman as an adult admired his dad for having such a deep insight.
That's got to be one of the most insightful responses I have ever seen here. BRAVO!!!!

We humanoids are pretty good at explaining activity that we observe (gravity, radioactivity,electromagnetism,etc) , and that enable us to make pretty good predictions in many areas of science, but "why" something is the way it is and not some other way is not so easy...that's why I sign off as I do:
 
  • #14
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But! how do we know when a reference frame is inertial or not
First things first: to know whether a reference frame is inertial or not, you just measure it ;-) You can measure acceleration using an accelerometer.
That's exactly right. Sometimes, though, you don't have the luxury of having an accelerometer traveling at constant velocity with respect to the inertial reference frame. More generally, any system of particles has an inertial frame. (This is what Newton's first law means.) However, the system is not obliged to have any particles in it traveling at constant velocity.

Consider two stars orbiting each other, for example. The system does have a coordinate system that's inertial (it actually has many), but neither star is motionless in that system.

In principle, the way you tell whether a coordinate system is inertial is by Newton's third law. If you're in an inertial reference frame, then a particle can only be accelerating because of a force. Any by the 3rd law, there must be some other particle in the universe that's experiencing the equal and opposite force.

So, if you pick a candidate inertial reference frame, look for particles that are accelerating. If each acceleration can be explained by the corresponding accelerations of other particles, then your frame really is inertial. If you have unexplained accelerations, then your candidate frame is not inertial.
Your explanation of how to determine an inertial frame is true for hypothetical situations such as the thought experiment where the only objects are the objects in your frame. I think BobbyBears question concerns the real universe. For example, imagine that we have a frame of objects which are accelerating toward another unknown object outside the frame. In other words, our entire frame is accelerating (unknown to us) toward this object which is outside of our frame. Even before our frame reaches the outside objects http://en.wikipedia.org/wiki/Roche_limit" [Broken] there will be accelerations of our frame objects away from each other due to gravitational tidal forces from the outside object. In this case you would not be able to find an inertial reference within this frame (not even with the aid of an accelerometer) unless you expanded your frame to include the unknown object. And that's my reason for thinking that there is no perfect inertial frame (in the real universe). Unless it's at the center of the universe, wherever that is. :)
 
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  • #15
Your explanation of how to determine an inertial frame is true for hypothetical situations such as the thought experiment where the only objects are the objects in your frame. I think BobbyBears question concerns the real universe. For example, imagine that we have a frame of objects which are accelerating toward another unknown object outside the frame. In other words, our entire frame is accelerating (unknown to us) toward this object which is outside of our frame.
My intent was to show how to determine an inertial frame when Newton's laws are valid.

In the above, I think we're conflating the terms "frame" and "system", or perhaps getting confused by the overloaded term, "system." We have to take care to understand the two meanings of "system." It's unfortunate that we use the same term for different things.

A system can be a collection of objects under study. Or it can mean a coordinate system. One has to keep these two meanings straight. You can draw an arbitrary boundary around any objects you want. Then, the external object you're talking about is indeed outside the system (of objects). But it's still in the universe, and there's no reason why it can't be represented in the coordinate system.

So, suppose the object you're talking about is a big magnet pulling on the objects in the system, accelerating them. The objects are also pulling on the magnet with equal and opposite force, so it's accelerating too. In this way, the acceleration of the particles towards the magnet can be explained by the acceleration of the magnet towards the objects. In our thought experiment, the 3rd law can tell us that a well-chosen coordinate system is inertial.

Even before our frame reaches the outside objects http://en.wikipedia.org/wiki/Roche_limit" [Broken] there will be accelerations of our frame objects away from each other due to gravitational tidal forces from the outside object. In this case you would not be able to find an inertial reference within this frame (not even with the aid of an accelerometer) unless you expanded your frame to include the unknown object. And that's my reason for thinking that there is no perfect inertial frame (in the real universe). Unless it's at the center of the universe, wherever that is. :)
I'm afraid I'm not following that. An inertial frame does not mean that objects can't accelerate. It means that objects don't accelerate without explanation. Gravity is certainly a force that can accelerate the objects, so the presence of gravity does not destroy an inertial frame.
 
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  • #16
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Yeah, I think you misunderstood. I was not trying to say that objects cannot accelerate in an inertial frame. I was trying to give a thought experiment (carried to the extreme) to show why a perfect inertial frame could not exist in the real universe. We can have inertial frames that are more than accurate enough for our needs, but none can ever be perfect because all objects in the universe are linked in some way, and no inertial frame can completely isolate itself (unless it's in a thought experiment).

My thought experiment was based on the post made by slider142:
slider142 said:
Free fall is a great inertial frame, but only inasmuch as the frame doesn't last long enough for the force differential to be noticeable between objects closer to the center of gravity versus objects further away. Most "inertial" frames have some type of limit on them, either time or position.
Also, I disagree with yours and diazonas argument that an accelerometer can be used to determine if an object is accelerating. If an accelerometer is accelerating in free-fall it will indicate zero.
 
  • #17
Yeah, I think you misunderstood. I was not trying to say that objects cannot accelerate in an inertial frame. I was trying to give a thought experiment (carried to the extreme) to show why a perfect inertial frame could not exist in the real universe. We can have inertial frames that are more than accurate enough for our needs, but none can ever be perfect because all objects in the universe are linked in some way, and no inertial frame can completely isolate itself (unless it's in a thought experiment).
Thanks for the thoughtful response. Yes, you are right, I did misunderstand. And honestly I still don't really understand. Newton's first law is the assertion that inertial frames exist. It's a claim about the way the world works. Perhaps you are misusing the term frame to mean system of objects? Inertial frames are certain coordinate systems, not systems of objects. (Again, there's that frustrating problem that the word system has two meanings.) So, there is no need for an inertial frame to completely isolate itself, nor do I really understand what that could mean.
 
  • #18
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Thanks for all your insightful responses! : ) Though to be honest some of the things laid out are somewhat hard for me to grasp as I'm not a physicist.

I'm not sure why we are considering systems of particles . . .

Like why, Turtle, you'd want to choose the centre the mass of our universe as our intertial reference frame. Is this because you're considering that being at the centre of mass would mean that the net gravitational attraction force upon a particle that sat at the centre of mass of the universe would be nil and thus would have no reason to accelerate?

Why, Cantab, are we talking about systems of particles having or not intertial reference frames?

I'm thinking of a reference frame as a coordinate system, which exists whether or not there is a mass attached to it. And I think my question was more basic, I wasn't really thinking about what causes real accelerations of material bodies . . . according to Newton's third law, the accelerations have to come in pairs, so as Cantab said, if one body is accelerating due to another body's gravity, the other body must experience the same attractive force towards the first body . . . which is kind of like stating the conservation of linear momentum principle for a system of particles upon which there is no external force applied, the system being our universe. Which is really again just an application of Newton's second law..

I wasn't really thinking of 'real' forces, my quandary is with Newton's second law itself, not in accepting it and then trying to figure out whether it is applicable or not in a certain reference frame (ie finding out whether the reference frame is or not inertial). What I mean by not 'accepting' it (not quite the right word:P, rather, understanding its implications), is, that Newton's second law relies on first defining what an inertial frame of reference is, ie, in an inertial frame of reference, F=m*a. But then it happens that a reference frame is inertial if Newton's law holds for an observer moving with that reference frame, and if it doesn't hold and there are 'unexplained' accelerations (ie. not due to real forces) to an observer moving with that frame, then it is a non-inertial frame. So now the concept of what an inertial frame is is based on whether or not Newton's law holds in the said frame! So the concepts depend upon each other?

Can the concept of inertial reference frame be defined prior to any application of Newton's laws?

How can we define inertial frame as one which is not undergoing acceleration if the concept of acceleration is a relative one? (is it? . . . like when you're looking out of a train window and the train starts moving, if the movement is sufficiently smooth so that you don't feel the thrust, you get the sensation by looking out that it is you who are still and the world is moving backwards instead of the other way around. Sort of, am I accelerating with respect to you or is the other way around?).

I'll try and explain my thoughts with examples.

Let me first consider that Newton's law is a universal law and there is such a thing as an absolute inertial frame (in the sense that it is not accelerating . . . though as I said, I think such a concept is vague). And for example, imagine the Earth (and all the known universe) was accelerating with a large linear acceleration "A" (due to a real force . . . which I've no idea whence originates). Of course, any frame attached to our movement Would be non-inertial. Thus we'd all be subject to a ficticious force. So we'd write, F-Ff = m*a, where Ff is the ficticious force we're all subject to. Would we be aware of it? I'm not exactly sure how an accelerometer works, but from what I've read, basically it consists of, considering only a single direction, a spring attached to a mass suspended inside a box, and what we measure to detect acceleration is the displacement of the mass from it's position of equilibrium, ie. the variation of length of the spring, which exerts a real force upon the mass to compensate the ficticious force that the acceleration provokes. But in this case, the position of equilibrium would already take into account the ficticious force we're all subject to, and we'd only measure relative acceleration with respect to "A". So it wouldn't really give us information as to the fact that our world is accelerating . . . would it? So would we still be able know that our world is accelerating? If all our mathematical descriptions of nature implicitly took into account the ficticious force we're subjected to, would we still feel it or would it manifest itself somehow? Could we be writing Newton's law as F'= m*a, not realising that F' is really F-Ff? I guess my reasoning on this is flawed but I'm not sure exactly how..


But on another line of thought, I find myself wondering the following: suppose the Earth and the known universe was moving in some very complex but determined fashion, at least with respect to some other part of the universe, because I'm not sure if there is such a thing as absolute movement. That is, it may be accelerating, or the acceleration be non-uniform . . . a movement that's however complex you like, but precise. Now, barring the effects of the centrifugal force caused by the Earth's rotation about its axis and all such minor effects, Newton's second law, as he devised from observing the world around him, works perfectly in a reference frame attached to Earth. Then this reference frame IS inertial, simply by definition, but it doesn't mean that the Earth is not accelerating. It just means that Newton's law defines what an inertial reference frame is, and by definition, the Earth is one. And any reference frame that is accelerating differently to Earth is non-inertial. If there is such a thing as absolute acceleration, then if this was true, in a reference frame that was truly not accelerating, Newton's law would not hold, and I don't only mean because there'd be ficticious forces to consider - simply no. Could this be why Newton's law works in a reference frame attached to Earth: not because the Earth is not accelerating, but simply because Newton's law happens to work (without anyone being able to explain why) in a reference frame that is moving with the precise (yet unknown) way the Earth and the surrounding universe is, and as such, serves to define a concept of force and acceleration that are only valid in this frame. Thus Newton's law would not be a universal law at all, though we'd have no way of knowing that, but we'd not have to find ourself struggling to believe that of all the possible and infinitely complex ways in which it could be moving, the Earth and the universe surrounding it is moving with constant speed.

Lol someone show me how this doesn't make any sense?:P:P
 
  • #19
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BobbyBear said:
Thanks for all your insightful responses! : ) Though to be honest some of the things laid out are somewhat hard for me to grasp as I'm not a physicist.
I'm not a physicist either so please don't consider my posts in that respect. I'm just a guy who is interested in classical physics and gravity in particular. Anything I say is subject to being wrong. Please correct me if you think I'm wrong, as I am interested in learning also.

BobbyBear said:
Like why, Turtle, you'd want to choose the centre the mass of our universe as our intertial reference frame.
That was meant to be in humor so that's the reason I used the smiley face. According to current theories there is no center of the universe.

The universe does not come with a built in coordinate system. We build our coordinate system to fit our frame. If we do not have to invent fictitious forces to explain the motions of objects in our frame then it is inertial.

Remember what I said about there being no perfect inertial frame? Let me give another thought experiment.

We have our frame set on planet Earth, maybe in a lab or something. We know about the Earths gravitational force so we account for that. Using our lab instruments we can calculate the movements of all the objects in our frame by using Newtons laws. Everything checks out, so we can assume that our frame is inertial. We happily go about doing our experiments knowing that our frame is inertial. But then someone brings in some new and much more sensitive instruments. With the new instruments we discover that something is wrong. Our objects are slightly off from what Newtons laws predict. Upon further investigation it is found that the unusual motions seem to follow a somewhat monthly cycle. Of course it is the moon that is causing the discrepancies. But since we really want to make use of the new higher precision instruments we must either account for the moon the same way we do for the Earth, or we must expand our frame to include the Earth moon system.

As illustrated in the thought experiment, no inertial reference frame can be perfect because all things in the universe are linked in some way. But because local effects are much more prominent, we can account for the local effects and have a frame that is close enough to inertial for our needs.

Since there is no perfect inertial frame, it is not necessary that an inertial frame be non-accelerating, as long as all objects in the frame are accelerating at the same rate and direction. In fact it would be practically impossible to have a totally non-accelerating frame, unless it was at the non-existent center of the universe. :)

To sum up, I think this is the best one sentence definition I've seen of what defines an inertial frame:
The identification of an inertial frame is based upon the simplicity of the laws of physics in the frame. In particular, the absence of fictitious forces is their identifying property.

from: John J. Stachel (2002). Einstein from "B" to "Z"
 
  • #20
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With the new instruments we discover that something is wrong. Our objects are slightly off from what Newtons laws predict. Upon further investigation it is found that the unusual motions seem to follow a somewhat monthly cycle. Of course it is the moon that is causing the discrepancies. But since we really want to make use of the new higher precision instruments we must either account for the moon the same way we do for the Earth, or we must expand our frame to include the Earth moon system.
I'm not sure I follow, when you say "account for moon", do you mean to say that we must account for the acceleration upon the Earth caused by the Earth-Moon system, because you're considering our reference frame to be moving solidarily to the Earth?

And about:
it is not necessary that an inertial frame be non-accelerating, as long as all objects in the frame are accelerating at the same rate and direction. In fact it would be practically impossible to have a totally non-accelerating frame, unless it was at the non-existent center of the universe. :)
. . . you're saying that in practice, any reference frame linked to a body must accelerate because there is a net force acting upon that body (unless that body is at the centre of the universe), but that acceleration is "arbitrary" or relative, to put it in some way, because we've not yet defined who is accelerating with respect to whomm . . . and we on that body would not have knowledge of that acceleration and so we'd consider it an inertial reference frame? And Newton's law would hold in our "relatively accelerating" frame because the law defines that our frame is inertial?
 
  • #21
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BobbyBear said:
I'm not sure I follow, when you say "account for moon", do you mean to say that we must account for the acceleration upon the Earth caused by the Earth-Moon system, because you're considering our reference frame to be moving solidarily to the Earth?
Yes, I am referring to the moons gravitational effect on the Earth which includes our objects in the lab frame of the thought experiment. I'll refer you to this thread: https://www.physicsforums.com/showthread.php?t=314993 It's not exactly what we're talking about here but it may help you understand the Earth moon system a little better. Pay particular attention to the post by DH. In the same way that the moon affects our oceans tides it will also affect our objects in the lab frame. It was this effect that the new more sensitive instruments in the thought experiment were able to detect.
BobbyBear said:
you're saying that in practice, any reference frame linked to a body must accelerate because there is a net force acting upon that body (unless that body is at the centre of the universe), but that acceleration is "arbitrary" or relative, to put it in some way, because we've not yet defined who is accelerating with respect to whomm . . . and we on that body would not have knowledge of that acceleration and so we'd consider it an inertial reference frame? And Newton's law would hold in our "relatively accelerating" frame because the law defines that our frame is inertial?
Not exactly. But that's close enough. It's not the fact that we have not yet defined who is accelerating with respect to whom (it doesn't matter), it is the fact that the effects due to accelerations from non local objects are too small to have an impact on our calculations and measurements. But just because we cannot detect the non local effects does not mean they are not there. And that's the reason for my statement that there are no perfect inertial frames. Or as slider142 said "Most inertial frames have some type of limit on them". However, I would argue that ALL inertial frames have some type of limit.
 
  • #22
I'm thinking of a reference frame as a coordinate system
Yes, I believe that is exactly right. It's a special coordinate system. There are zillions of possible choices of coordinate systems. The inertial ones are those in which Newton's second law holds.

I wasn't really thinking of 'real' forces, my quandary is with Newton's second law itself, not in accepting it and then trying to figure out whether it is applicable or not in a certain reference frame (ie finding out whether the reference frame is or not inertial). What I mean by not 'accepting' it (not quite the right word:P, rather, understanding its implications), is, that Newton's second law relies on first defining what an inertial frame of reference is, ie, in an inertial frame of reference, F=m*a. But then it happens that a reference frame is inertial if Newton's law holds for an observer moving with that reference frame, and if it doesn't hold and there are 'unexplained' accelerations (ie. not due to real forces) to an observer moving with that frame, then it is a non-inertial frame. So now the concept of what an inertial frame is is based on whether or not Newton's law holds in the said frame! So the concepts depend upon each other?
It's natural to be troubled by the apparent circularity of Newton's laws. There are some books out there that don't help matters either. You might even read someplace that Newton's first law is just a special case of the second, where you plug F=0 into F=ma. But that's not really reflecting what Newton was driving at. Ernst Mach looked at Newton's laws, and tried to restate them in a more "modern" way. Mach's reformulation is said to have influenced Einstein.

I certainly do not compare myself to Mach, but here's the way I think about it...

An inertial reference frame is a coordinate system in which unperturbed objects do not accelerate. The first law is a claim about the universe: that such frames exist.

The second law, [itex]F=dp/dt[/itex], tells you how objects behave in an inertial reference frame. It also asserts that force is a useful concept. One could imagine that the world obeys a different differential equation, say [itex]X=d^2p/dt^2[/itex] for some weird function X. In fact, there's nothing that would prevent you from doing that. However, that X would be incredibly complicated, and wouldn't be too useful. Nature however gives very nice expressions for force F, when the force is gravity, or friction, or whatever. The magic of the second law is not in the right hand side (ma), it's in the left hand side, F.

The third law allows you (in principle) to tell whether any given frame is inertial. By the 3rd law, any unexplained accelerations would tell you that your frame is not inertial. So, it's the 3rd law that allows you to escape the circularity. You need all 3 laws for conceptual consistency.

Remember what I said about there being no perfect inertial frame? Let me give another thought experiment.
TurtleMeister, you offer examples where objects accelerate because of forces. I don't follow the logic of how that invalidates the inertial-ness of the frame. One happy thing about the universe, though, is that all forces fall off with distance. So we can neglect some of them because their influence is vanishingly small. But that's more a statement about the nature of forces than about whether the concept of inertial frames is valid.

Since there is no perfect inertial frame, it is not necessary that an inertial frame be non-accelerating, as long as all objects in the frame are accelerating at the same rate and direction.
I'm sorry, I don't see how that follows at all. If a frame is accelerating, how can it be inertial?
 
  • #23
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Cantab Morgan said:
TurtleMeister said:
Remember what I said about there being no perfect inertial frame? Let me give another thought experiment.
TurtleMeister, you offer examples where objects accelerate because of forces. I don't follow the logic of how that invalidates the inertial-ness of the frame.
The intent of my thought experiment was not to invalidate the inertial-ness of a frame where the objects accelerate. Either you misinterpreted or I was unable to convey my thoughts. Most likely the latter. :) The intent was to show that there can be no perfect inertial frames in the real universe. Being imperfect does not invalidate the inertial frame.

I know that you think I am confusing a reference frame and a system of objects. And maybe I am because I don't really understand that argument. Any frame will always contain a system of objects. If the inertial frame is the coordinate system, then what is the coordinate system relative to? How do you determine that? The universe does not have a center and it does not have a coordinate system. So wouldn't it have to be relative to an object or the center of mass of a system of objects?

Cantab Morgan said:
TurtleMeister said:
Since there is no perfect inertial frame, it is not necessary that an inertial frame be non-accelerating, as long as all objects in the frame are accelerating at the same rate and direction.
I'm sorry, I don't see how that follows at all. If a frame is accelerating, how can it be inertial?
Sorry, I should have worded that to say that the frame and coordinate system are accelerating with the objects. The only requirement for an inertial frame is that there be no fictitious forces. If the frame and coordinate system are accelerating in a gravitational field (free-falling) along with all the objects in the frame then the frame and it's coordinate system could be inertial. That is until/if the frame, along with all it's objects, gets so close to the gravitating object that the effects from the tidal forces become apparent. In which case the effects would have to be accounted for or we must expand our frame to include the gravitating object and likewise change our inertial reference.
 
  • #24
Yes, I think we're having a little trouble understanding each other, but that's what makes exchanges with interesting people so enjoyable.

Frame and coordinate system are synonyms. What do you believe frame means? If I could understand that, then I could better see what you are driving at.
 
  • #25
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Cantab Morgan said:
Yes, I think we're having a little trouble understanding each other, but that's what makes exchanges with interesting people so enjoyable.
Yeah, my communication skills are not the best.

Cantab Morgan said:
Frame and coordinate system are synonyms. What do you believe frame means? If I could understand that, then I could better see what you are driving at.
I think of a frame as a square (2d) or cube (3d) with an attached xy or xyz coordinate system. And there are usually objects in the frame. Of course all that's really required is the coordinate system. But what's the point if there's no objects? Anyway, I don't think I have a problem with understanding reference frames. DH has drilled me pretty good on this in another thread. :)

As I was googling around I found this video on frames of reference. It's pretty old and quite simple but it was fun to watch. It's in four parts and the last part explains why we can be on the spinning Earth and still have an inertial frame (which is accurate enough for our needs). Which feeds right into what I was saying about there being no perfect inertial frame.

 
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