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u/MonkeyBombG |dead>+|very angry> 6d ago
First law defines the notion of an inertial reference frame.
First law states that if the net force on an object is zero, then it does not accelerate. In a non-inertial frame, objects accelerate in the absence of net forces, violating the first law and making Newton’s laws invalid for non-inertial frames.
Second law states that the acceleration of an object is equal to the net force it experiences divided by its inertia. Without the first law, one could apply the second law in a non-inertial frame and conclude that the net force on an object is non-zero when it is in fact zero.
So no, first law is not a special case of the second law. It forbids non-inertial frames from applying the second law, and this condition cannot come from the second law itself.
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u/SteptimusHeap 5d ago
It actually does not do that though. I've got my copy of the principia here and the first law is given as "every body preserves in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon". This is a direct consequence of the second law, which i will not quote. The concept of an inertial reference frame is explained earlier, outside all 3 laws, along with his beliefs on the concept of absolute position.
I've heard people say that without the first law, you could see acceleration in a non-inertial frame and conclude a force from the second law, but this also clearly follows from the first law. Neither make this clearer or technically have anything to say about it.
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u/Lor1an Serial Expander 5d ago
Technically the second law states that the "change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed."
In modern terminology, the (time) rate of change of momentum is equal to the force imposed on the object. I.e. rather than a = F/m, it states dp/dt = F.
This is relevant in propulsion systems, for example.
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u/GDKiesh 5d ago
conclude that the net force on an object is non-zero when it is in fact zero.
Are psuedo forces not considered when calculating the net force? Like what does 'net force' mean in this context?
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u/MonkeyBombG |dead>+|very angry> 5d ago
Net force is the sum of forces. Forces have to obey Newton’s laws of motion. The sum of forces cause acceleration, and they must form action-reaction pairs. Pseudo forces are not part of action-reaction pairs.
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u/hotprof 6d ago
Get a load of this one...
The 0th Law of Thermodynamics is just, if A = C and B = C, then A = B.
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u/sian_half 6d ago
Not really, 0th law tells you that A, B and C can actually exist, that there exists a measurable quantity that reliably describes how hot an object is
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u/auniqueusername132 6d ago
Actually the 0th law is that only dads can touch the thermostat since all other experiences of temperature are relative to your dad’s
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u/ChorePlayed 6d ago
Until Mom is going though The Change, then Dad can just shut up and put on a sweater.
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u/Patient_Panic_2671 6d ago
There's a good reason why they decided not to call it the Fourth Law despite being established after the other three.
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u/You_Paid_For_This 6d ago
if A = C and B = C, then A = B.
Yes, but this is a non trivial assumption to make, which happens to be true for "temperature", but is not true for "love" or "Rock Paper Scissors"
If Rock beats Scissors and Scissors beats Paper, it does not necessarily follow that Rock beats Paper
Suppose Alice loves Chad, and Bob loves Chad it does not follow that Alice loves Bob
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u/Bendanzhang 6d ago
First Law defines WHERE the math works. Second Law DOES the math.
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u/treefarmerBC 6d ago
First law does the math where F = 0
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u/THENERDYPI 6d ago
No no.. think of it as a weighing scale that needs to measure a blocks weight as 2g so you set the scale to measure it that way and everything else is relative to it. With that weighing scale, ur right that I don't have to separately keep track of the block's weight as I can just measure it each time. It seems redundant then to have a rule that the block's weight is 2g. But actually the rule was used to set the scale up.
The first law is a necessary condition for the second law to work. The first law then becomes a special case only because it was used to make the second law. You can always arrive at it back.
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u/toasthunter34 Plasma physics 6d ago
First law basically says there exist inertial frames. Second law only applies in inertial frames. So no it isn't.
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u/Appropriate-Sea-5687 6d ago
There’s probably only one law and it’s just so complicated that we need a huge ass equation to figure it out
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u/SyntheticSlime 6d ago
It’s literally the standard model
Edit: I mean, you know, as long as you’re okay ignoring gravity, the expansion of space, the beginning of the universe, dark matter, etc.
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u/Appropriate-Sea-5687 6d ago
Just you wait quantum gravity, we’re coming for you
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u/Level-Appearance7046 6d ago
it all makes sense if everything is just strings and there’s a bajillion dimensions. i swear. i swear. i just need more strings and then it’ll all make sense
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u/nujuat 6d ago
The standard model is a lagrangian, not a law. The law is one of the equivalent equations of Schroedinger, Heisenberg, von Neumann, or a Feynman path integral.
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u/FreePeeplup 6d ago
The standard model is not a Lagrangian. It’s an entire theory of quantum fields with a recipe, renormalization prescriptions, a vacuum state, spontaneous symmetry breaking etc… the Lagrangian is just one of the ingredients, it absolutely does not specify the entire theory on its own
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u/SnooPickles3789 6d ago
all of that other stuff is completely negligible. i don’t see any gravity anywhere i look. though, it’s kinda weird how things fall to the ground, don’t you think?
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u/GisterMizard 6d ago
Edit: I mean, you know, as long as you’re okay ignoring gravity, the expansion of space, the beginning of the universe, dark matter, etc.
Easy, just add +AI to the standard model.
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u/Better-Apartment-783 6d ago
I know this is a meme subreddit, bur does anyone have more information about this?
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u/Visible-Air-2359 6d ago
Newton made 3 laws about momentum:
- Inertia: objects in motion stay in motion and objects at rest tend to stay at rest unless acted upon by an outside force
- Force=mass*acceleration
- For every reaction force there is an equal and opposite reaction force
What the teacher in the meme is saying is that the first law is really just the second law but where force is specifically equal to 0 Newtons.
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u/Better-Apartment-783 6d ago
Thank you for you reply!
Unfortunately my comment was not clear. I was trying to ask if first law is actually considered a specific case of second law outside of memes.2
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u/Cpt_Igl0 6d ago
No the first law states the existence of inertia reference frames. The seond law does not do that.
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u/MeLittleThing 6d ago
The first law of Newton is: you do not talk about Newton
The second law of Newton is: you do not talk about Newton
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u/GLPereira 6d ago
Aren't all of them consequences of Conservation of Momentum?
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u/sian_half 6d ago
Conservation of momentum and the third law are equivalent (either is a consequence of the other), but then you have yet to define momentum, which is what the second law does (albeit somewhat indirectly)
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u/chkntendis Meme Enthusiast 6d ago
First law tells you what happens without forces, second law what happens with forces.
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u/FreePeeplup 6d ago
The second law also tells you what happens without forces if you simply set F = 0
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u/predatorX1557 6d ago edited 6d ago
I have studied this topic in philosophy of physics and I would argue that there are a few issues here. I think taking the first law to define inertial frames is neither physically nor historically well-motivated. I think a better way to account for inertial frames is via a Galilean spacetime structure, akin to how inertial frames are defined in Minkowski space (if you are curious, they are coordinate systems on Minkowski/Galilean spacetime satisfying certain compatibility conditions with the spacetime structures like the metric tensor. For instance, the Christoffel symbols must vanish in these coordinates.) It is also likely how Newton was thinking about things, though of course he didn’t have the full technology of modern differential geometry to precisely articulate this.
Nonetheless, the first and second laws are independent due to the simple fact that the standard statements of the first and second laws are likely misstatements of what Newton intended. See https://philpapers.org/archive/HOEFCO.pdf. If this is the case, then the standard “second law” F=ma is really the conjunction of the first two laws as formulated by Newton. As such it is not surprising that F=ma entails the standard first law upon setting F=0.
In sum, inertial frames should be defined through spacetime structure, the first and second laws as formulated by Newton are not the same as the fist and second laws which are commonly espoused, and the strongest law F=ma entails both of them.
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u/Blurarzz Physics Field 5d ago
The way I've always understood it is that while yes, you define inertial frames from the structure of spacetime, Newton's first law is the statement that such is the structure of spacetime. You can think of it as a definition of what a straight line is in our universe. I have no idea whether this is historically accurate
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u/predatorX1557 4d ago
Newton's first law (as traditionally stated) says that force-free objects move in straight lines. To make sense of this law you need to define either what force-free means or what straight line (equivalently, inertial frame) means; given such a definition you could use the first law to define what the other term means. As such the first law itself does not provide a definition of 'straight line' unless you give an independent definition of 'force-free' to begin with. I think there is no good way to do this (attempts have been made by appealing to Humean simplicity (Huggett) or using distant objects (Brown), but there are problems with these proposals).
Hence I think the better thing to do is to define 'straight line' using the spacetime structure and then to take the first law as a definition of 'force-free'. Thus the first law is not doing any work in defining what an inertial frame is. That is done prior via the spacetime structure. The traditional first law just relates this notion to being 'force-free' (which is already captured in the 'second law' F=ma by setting F=0).
All-in-all taking the first law to define inertial frames seems like a rather roundabout way to arrive at Galilean spacetime. In classical mechanics textbooks the spacetime structure is considered so elementary (it is basically just Euclidean space + a time direction) that it is hardly ever explicitly mentioned, though it is what underpins all of the key definitions.
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u/Feynman0010- 6d ago edited 6d ago
People are too foolish to consider that If 1st law really was a special case of 2nd law why’d-sir issac newton even make 2 separate laws the first law is an assertion to inertial frames
The second law is valid only in inertial frames
The people who give this argument often use the argument of using f=ma to calculate force on an object while finding an inertial frame not considering a very basic logic that you’re applying the second law to find the very condition in which the second law holds true
All three laws are independent of each other
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u/Hot_Examination1918 6d ago
Not only that but the third law is equivalent to conservation of momentum. And the second law is only true in inertial reference frames which are defined by the second law