# Newton's first law

## Main Question or Discussion Point

HI,
I have a stupid question but important, Newton;s first law doesn't mention anything about Net force , just that a body that no external forces acts in him, will stay @ rest or with constant velocity ,now my problem is the word "rest",
Is a body at rest relative to something Is a body that relative to that thing has zero velocity? or body at rest means that there are no forces on him + relative velocity=0?
or no net force acts on him+relative velocity =0?
Like ,which conditions satisfy the word "Rest".
Let's say a body is thrown vertically , and at the top height it's relative velocity(according to me as an observer) =0 , can I say that this is a position that the body is @ rest? or it's false cause there is net force on him, I know that this period of relative velocity=0 is small, but in the moment cau I say the body is at rest?

to cut a long story short:
Does rest mean:
1)Rest in peace, aka no net force + relative velocity=0.
2)Rest in your couch, not moving just changing TV-channels ,aka just relative velocity=0?

thank You,
Dw

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Hi there,

I believe you think to much. "Rest" can be considered a constant velocity. In constant velocity is understood a speed that does not change, whether in size, nor in direction. "Rest" seams to fulfill these requirements, since v=0.

Newton's first law simply says that if you don't touch a body, it will not move. That's the ingenuity of scientists.

Cheers

It's more about the word rest and less about the first law,
is Rest defined just that the velocity of a body relative to other is 0?
IS rest defined by the first law or just common sense??
rest means that it always be with zero velocity relative to a body' isn't there an instant rest ?
thanks

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russ_watters
Mentor
Yes, rest is just a velocity of zero relative to something else. A ball thrown vertically is, for an instant, at rest at the top of its flight.

Hi there,

IS rest defined by the first law or just common sense??
Aren't the laws of physics about common sense??? I studied this field for many years, and theories had to make sense, otherwise.

Cheers

fatra2 and russ_watters
I was arguing with a friend about this, and I said exactly what russ said , and he said I'm wrong...and he made me believe I am XD well nvm ...
and fatra
The laws are based on common sense( most of them) but some definitions are not exact ,and are not used in the daily basis with recognition of what they really are, thus our common sense is built by a bunch of stigmas and definitions.
I can tell You that every person I asked thought that the first newton law is about that if the net force on a body is 0 than bluh bluh , which is true but not exact and not stated in the first law, the first law is made for creating a "play ground" for the physics laws, which no external forces act on .
many books are not stressing it enough , and things like that mg and N are not action-reaction pairs , and so on...
so thank you people.
and btw by common sense I meant that it just doesn't move in the moment i see it, which i may think it's in rest, although there is a net force on him, but in that moment hs is BASICALLY at rest(common sense). just wanted to know If i miss-understand the definition of rest.

If a body is at rest, it doesn't necessarily mean it has no force on it.

So point 2 is right.

Next time I'll just count on my knowledge and common sense, and not listen to other students minds :D

HallsofIvy
Homework Helper
A body momentarily at rest- that is a body such that it speed at time t0 is 0- does not have to have 'no net force' on it. But if there is a net force it will not stay at rest. Its acceleration is not 0 so it will immediately start moving.

yes of course , than it will accelerate (increasing\decreasing velocity, doesnt matter)and wont be in rest anymore, but can i say that in that short moment the body is at Rest?is this suitable for the definition of rest(as the answers I got say it does).?

D H
Staff Emeritus
The modern view of Newton's first law is that it defines the concept of an inertial frame. Imagine you are at an amusement park. You hop on a hair-raising ride while a couple of your chicken friends stays on the ground and stand still. Your friends are stationary with respect to the Earth and each other, but they are anything but stationary from your point of view. Your point of view is not an inertial frame.

Alright , acceptable , although I'm not in favor of involving inertial and non inertial frame, cause i can go really deep to this subject (such as , if earth is accelerated, although it's small, why is that an inertial frame ? and , inertial frame relative to what?) so I want to avoid that /
but anyway:
So did You try to say that If i'm shot into the air by a cannon and reach the top height I can go , in that moment , I won't see the ppl on earth stationary relative to me ?
Is there a difference between stationary and @ rest?
thanks.

D H
Staff Emeritus
Newton's first law is all about inertial frames. Pretend for a moment that the Earth is not rotating or acceleration toward the Sun, the Moon, and anything else. Those accelerations are pretty small, after all. The Earth can be treated as an inertial frame given sufficiently small periods of time, small distances, and small velocities.

Pretend for a moment that you are just a dumb robot, year 2050. Your owners sent you along with the kids to act as a baby sitter. The kids strapped you into the ride to see if you would freak out. You are just a dumb robot. All you know is that vector between you and your charges is constantly changing, and is doing so in a very non-linear fashion. What's making that vector swing around so radically? Is somebody pushing those kids around? You're just a dumb robot, remember; you don't know the difference between inertial and non-inertial frames.

thx for stressing 3 times im a dumb robot XD
forget for a minute I'm a robot,
so can You say the robot is an non-inertial frame relative yo the kids, or the kids are in a non-inertial frame relative to teh robot, or both, or neither?

D H
Staff Emeritus
The robot reference frame has origin at the robot's center of mass and axes fixed with respect to the robot's chasis. The position of the robot's charges (the kids) is anything but constant in this reference frame. If the robot (erroneously) tried to apply Newton's laws of motion in the reference frame the only conclusion the robot could come to would be that some strong forces are acting on those kids.

Newton's first laws of motion fails in the robot reference frame: It is not universally true. The modern view of Newton's laws is that the first law establishes the framework in which the second and third laws are valid. After all, the rest of this law is trivially true. That things at rest stay at rest is merely a special case of a constant velocity, and the constant velocity is a simple corollary of the second law.

So could one say that newton's second law is not valid for non -inertial frames?
thanks for ur help :+)

D H
Staff Emeritus
So could one say that newton's second law is not valid for non -inertial frames?
thanks for ur help :+)
Newton's second law in its canonical (simplest) form is

$${\boldymbol F_{\text{net}}=\frac{d{\boldymbol p}}{dt}$$

Newton's second law can be used in non-inertial frames, but in order to do so one must add in some correction terms. These correction terms have various names depending on the nature of the reference frame: inertial force (the origin is accelerating), centrifugal force (the frame is rotating), coriolis force (the frame is rotating and the object is moving), and euler force (the frame is rotating non-uniformly). The collective term for all of these correction terms is fictitious forces:

$${\boldymbol F_{\text{ext}} + {\boldymbol F_{\text{fictitious}}=\frac{d{\boldymbol p}}{dt}$$

These fictitious forces aren't real. They're a fiction. A very useful fiction at times.

Great,
that's exactly what Einstein said, You just need to construct a bridge between the frames :D
by applying the equivalence principle ,you can make an non inertial frame to have friendship with the physics laws :D
I used those fictitious forces more than once , but the equivalence principle is awesome for accelerated frames :D
well thanks for your help and the interesting discussion !
Dw

Dweirdo said:
Next time I'll just count on my knowledge and common sense, and not listen to other students minds :D
No no...don't do that...don't live on assertions, cause most probably they ARE wrong.

In physics many thing behave against your, or in general human expectation.

Like aaaa...the Linux kernel (though its not physics), its concept is out of the very imagination of our best possible assertions.

I know what You mean ... but sometimes it's good to have some assumptions and than prove it :d

I think ur already dun...but I think this should b mentioned so I've replied ..heres what I wanna say:
Rest means strictly at rest..a body moving @ constant velocity can b considered to b at rest with respect to another frame moving witth same velocity...then only it comes to rest in this new frame..
ans in Newtons Law...its clearly mentioned "If no external force acts on a body at rest/moving with constant velocity...." ....
so u dont need to bring/care the body at constant velocity at rest in some other frame...but u cant call it at rest in the original frame..and Newton's First Law" is still applicable...in the original & new frame

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There is no perfect inertial frame. How perfect it is depends on how accurate it is your measurement of time and space. The same can be said of an object at rest. If you're standing on earth and you throw an object upward, gravity will continuously accelerate the object until it comes back to earth. There is no pause at the top. Or, there is no unit of time that is short enough to define that pause. However, if you have a set limit on your time intervals and your measurement of distances then you can say that the object is at rest relative to you as long as it falls within those limits. And it is because we have such limits that we can use the earth as an inertial reference frame even though it's not.

RonL
Gold Member
There is no perfect inertial frame. How perfect it is depends on how accurate it is your measurement of time and space. The same can be said of an object at rest. If you're standing on earth and you throw an object upward, gravity will continuously accelerate the object until it comes back to earth. There is no pause at the top. Or, there is no unit of time that is short enough to define that pause. However, if you have a set limit on your time intervals and your measurement of distances then you can say that the object is at rest relative to you as long as it falls within those limits. And it is because we have such limits that we can use the earth as an inertial reference frame even though it's not.
I need to ask a question here. Is my thinking right or wrong? If the ball is thrown perfectly straight up, there has to be a moment of complete rest as discussed, however if it has the slightest bit of an arc, it will follow the exact same rules of a flywheel and what I believe is refered to as zero point energy.

There is no perfect inertial frame. How perfect it is depends on how accurate it is your measurement of time and space. The same can be said of an object at rest. If you're standing on earth and you throw an object upward, gravity will continuously accelerate the object until it comes back to earth. There is no pause at the top. Or, there is no unit of time that is short enough to define that pause. However, if you have a set limit on your time intervals and your measurement of distances then you can say that the object is at rest relative to you as long as it falls within those limits. And it is because we have such limits that we can use the earth as an inertial reference frame even though it's not.
Hi, TurtleMeister. You're using a non-standard and slightly misleading definition of the word "frame" here. A frame is not a finite enclosure of volume that contains objects. A frame is a coordinate system. The whole universe is in a frame.

You are quite right to say that the Earth is only an approximation of a perfect inertial reference frame. This is because the planet is accelerating around the Sun, and so forth. But Newton's 1st law is the assertion that inertial frames are real. The choice of a particular coordinate system that's only approximately inertial is not proof that no true inertial frame exists.

Well I got a satisfying definition of rest, of a good physics expert, as long as the body doesn't change his location relative to you, it is @ rest relative to you.
I.E
A Communication satellite ,relative to a specific point on earth , it is @ rest, though there is a nest force on the satellite and the relative LINEAR velocity is not 0.
sounds convincing :} and changes some things...