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Why a Ball remains stationary

  1. Apr 26, 2009 #1
    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?
  2. jcsd
  3. Apr 26, 2009 #2
    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.
  4. Apr 26, 2009 #3
    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.
    Last edited: Apr 26, 2009
  5. Apr 26, 2009 #4
    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.
  6. Apr 26, 2009 #5
    I saw that in a documentary about Feynman and it resonated with me, too. Life is a mystery.
  7. May 15, 2009 #6
    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
    dv/dt=0, velocity remains constant
    since ball was at rest it continues the state v=0
    Last edited: May 15, 2009
  8. May 16, 2009 #7

    *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 :)
  9. May 16, 2009 #8


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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 ;-)
  10. May 16, 2009 #9
    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
    But the accelerometer will not work if it's accelerating (free-falling) due to gravity.
  11. May 16, 2009 #10
    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.
  12. May 16, 2009 #11
    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
  13. May 17, 2009 #12
    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.
  14. May 17, 2009 #13
    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:
  15. May 17, 2009 #14
    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. :)
    Last edited by a moderator: May 4, 2017
  16. May 17, 2009 #15
    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.

    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.
    Last edited by a moderator: May 4, 2017
  17. May 18, 2009 #16
    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:
    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.
  18. May 18, 2009 #17
    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.
  19. May 19, 2009 #18
    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
  20. May 19, 2009 #19
    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.

    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:
  21. May 19, 2009 #20
    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:
    . . . 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?
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