# Which condition exactly does Newton's First Law of Motion apply?

As I was reading about Newton's First Law of Motion from some textbook, I noticed some detail that seemed to conflict with another textbook which I have read previously. Book 1 provided the following statement for the law:

In the absence of external forces and when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line).

Furthermore, to prevent misconceptions, Book 1 even made sure to emphasize this detail regarding when the law applies :

Newton’s first law does not say what happens for an object with zero net force, that is, multiple forces that cancel; it says what happens in the absence of external forces. This subtle but important difference allows us to define force as that which causes a change in the motion. The description of an object under the effect of forces that balance is covered by Newton’s second law.

However, Book 2 on the other hand has this to say:

Law of Inertia. States that a particle remains at rest or continues to move with uniform velocity (in a straight line with a constant speed) if there is no unbalanced force acting on it.

Newton’s first law is a consequence of the second law since there is no acceleration when the force is zero, and so the particle is either at rest or is moving with constant velocity.

Now it seems to me that these two sources conflict with each other, in particular, the condition of whether the law applies strictly in the absence of any external forces, including forces that balance out, or whether it still applies as long as there is no net force. Also, Book 2 implies that Newton's First Law is a special case of the Second Law where acceleration is zero whereas Book 1 seem to treat the two as separate things.

My question is which one should I follow? Is one correct and the other wrong? Or does the difference even matter at all?

Edit: For those who are curious about the books I'm referring to, here they are:

(1) Serway, R. A., & Jewett, J. W. (2013). Physics for Scientists and Engineers with Modern Physics (9th ed.). Cengage Learning.

(2) Hibbeler, R. C. (2016). Engineering mechanics: statics. Pearson Education India.

• "Or does the difference even matter at all?" It doesn't matter.
– hft
Commented Jul 21, 2022 at 4:32
• Does this answer your question? Why is Newton's first law necessary? Commented Jul 21, 2022 at 4:35
• @hft if you are saying that a reasonable understanding of the physical content of Newton's principles doesn't matter, I do not agree. Commented Jul 21, 2022 at 4:36
• @hft I do not see where you read that the OP is not attempting to obtain a reasonable understanding of the law. I see a reasonable question on a very specific conceptual point originating from the point of view expressed in two textbooks. Commented Jul 21, 2022 at 4:45
• @JohnRennie, I think you should have read more carefully this post. Even if there could be some connection with the independence of the first law on the second (in particular in the case of the second citation), it is a different conceptual question that would deserve an appropriate answer. I do not understand why this rush to close questions. I'll vote to reopen it. Commented Jul 21, 2022 at 4:56

Straight from Newton's mouth:

The first law:

Every body perseveres in its state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change its state by forces impressed.

(Emphasis added, to indicate the ostensibly new concept at the time of impressed force.)

The second law:

A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.

Newton did not write "$$\vec F=m\vec a$$," but this is the modern way we express his second law (or if you please, some combination of his first and second laws).

If you would like to read a lengthy explanation of what his words mean, please see this good reference.

My question is which one should I follow?

It doesn't matter. Just learn how to use physics to solve actual problems.

Is one correct and the other wrong?

No, not really. Both are fine. The passages you quote are using some extra words to try and explain pedagogically to a new learner. Don't read too much into the details of either passage. Think about how you would re-write each of Newton's laws if you wanted to explain them to a modern child. You would change some of the language, you would add a bit of color. You can do a lot of different things to try and explain the meaning of his words with other words. Ultimately, it is probably best to show the meaning rather than to say. When we write a lot of explanatory words, I think we are often trying to say in words what is better shown by demonstration.

Or does the difference even matter at all?

No, not really.

• I don't think I can say that I am satisfied with this answer. Sure, different people have different ways of explaining concepts but they should never contradict each other. In this case, the first author went out of his way to "clarify" the detail that I emphasized in this post (i hope you've read all of it) but the second one seemed to go against that very detail that the first author made effort to highlight. It's not merely a matter of using different or additional words; it's a matter of conflicting ideas. With the way both authors presented their ideas, I don't think both can be correct.
– Niko
Commented Jul 25, 2022 at 7:08
• In essence, what I'm asking is: is the absence of external forces the same as zero net force in the context of Newton's first law? If yes, that means the first author is outright wrong about his "clarification" and if the answer is no, the second is. They're not mutually inclusive.
– Niko
Commented Jul 25, 2022 at 7:14
• No, the "absence of external forces" is not the same as "zero net force." For example, you could have two people of equal strength pushing on opposite sides of a crate. The crate doesn't accelerate because there is zero net force. But there are clearly external forces, they just happen to exactly cancel. The acceleration in both cases is zero.
– hft
Commented Jul 25, 2022 at 12:56
• So if the two are indeed different but have the same effect (zero acceleration), does Newton's first law work for only one of the conditions and not the other? or can it be applied for both scenarios?
– Niko
Commented Jul 26, 2022 at 8:33
• @Niko , newton's first law is in fact a derivation of the second(ironic then that its called the first law). As the second author says, it is in fact a special case. However, the point here being that the first law works only under conditions where there is no change in its velocity(acceleration is 0, which only happens when either there is no force or forces are equal and opposite). Therefore, the point is that 0 can be written as simply 0(no external force) or x-x(no UNBALANCED external forces) Commented Jul 31, 2022 at 16:20

I think the questioner's point is very important and understandable that a clear distinction should be made between a situation in which no external force acts at all and one in which the net force is zero. It would be difficult to determine exactly which conditions the first law applies because several standpoints seem to exist for interpreting the significance of the 1st law, but the following is my consideration for the questioner’s point.

As the questioner mentioning, in Principia, Newton's first law of force is not described as a net force. The law of inertia is essentially considered to be a law about the motion of isolated object in an idealized situation where no external force acts, i.e., no interaction with another object. If the net force is included in the first law, for example, a situation in which an external force is applied against the dynamic friction force acting on an object (two forces are balanced and net force becomes zero) to produce a constant velocity linear motion would also be called inertial motion, but I find it difficult to readily understand that this is called inertial motion (recalling Galileo's original thought experiment on inertial motion). Instead it is understandable that stationary or constant velocity linear motion when the net force is zero is due to the second law.

On the other hand, if we take the viewpoint that the first law is a special case or consequence of the second law, the motion in a situation where no external force acts at all and that in a situation where the net force is zero are both due to the second law (or both due to the first law). From such standpoint, the first law is regarded merely as a law that defines the inertial frame of reference, so inherent nature of isolated object in free motion may not be given special meaning. However, I think the first law has the significance not only defining the inertial frame of reference, but also has the significance of clarifying the essential nature of the object's state of motion by explicitly state that an object is in stationary or constant velocity linear motion under no external forces.