# What is the point of Newton's First Law?

1. Apr 10, 2007

### Hyacinth42

What is the point of Newton's First Law? The first law says that "The state of motion of an object will not change unless acted upon by an outside force". In layman's terms, this means that the object's velocity wont change unless there is a net force (at least that is how our physics teacher explained it to us). In other words, if there is a net force on an object, there will be acceleration... Now, Newton's Second Law state "The net force on an object is equal to its mass times its acceleration. Newton's Second Law does not say the same thing as Newton's First Law. The first law states the concept, and the second law states the equation that applies to the concept. If the equation is correct, then obviously the concept exists. So, what is the point of Newton's First Law? Why can't we simply use the second and third law?

2. Apr 10, 2007

### cesiumfrog

I think it's largely historical. From a modern point of view, it seems obvious that there's a redundancy there: the third also nearly implies the first, and the second arguably does nothing except define a term (force).

But previously people might justifiably have assumed, for example, that an object in motion will naturally slow down and stop, that a constant force is required to produce constant velocity.

3. Apr 10, 2007

### christianjb

N2L also doesn't tell you whether a system not under the influence of external forces is allowed to move at a constant velocity or not.

It's possible to set up a 2nd order differential eqn. which obeys the 2nd but not the 1st law.

d2x/dt2=F/m
dx/dt=B+f(x) (at time zero)

4. Apr 10, 2007

### cesiumfrog

What are you trying to say? Your example *is* under external force (F=m(B+f)df/dx); clearly F=ma implies that zero force upon a (nonzero) mass gives rise to zero acceleration (hence constant velocity).

Last edited: Apr 10, 2007
5. Apr 10, 2007

### Stingray

You can think of the 1st law as defining the inertial references frames in which the 2nd law should be applied.

6. Apr 10, 2007

### christianjb

I didn't express myself very well there.
The equation is correct. I said 'at t=0', so it doesn't make any difference to N2L.

Imagine though that the rule were that all particles in zero external force are moving with a velocity dx/dt=0. That's still consistent with N2L, but it doesn't admit non-zero velocity solutions.

7. Apr 10, 2007

### christianjb

I think that's probably the best answer.

8. Apr 11, 2007

### lpfr

Cesiumfrog is correct. This is just an historical matter. At the time of Newton, people knew that if you stop pushing a wagon, it will stop. Galileo found that, for objects gliding, time taken to stop depended on the polish of surfaces. At Newton's time, to said that an object does not need a force to rest in movement was as absurd and incredible as to say that the moon was in free fall, or that objects can attract at planetary distances. Yes, there is a redundancy and no, the first law does not define inertial reference frames.

9. May 3, 2007

### becko

10. May 4, 2007

### lpfr

From chapter I-9 of Feynman (Newton's Laws of Dynamics):
9-1, second paragraph:
"The First Law was a mere restatement of the Galilean principle of inertia just described."
.... "We shall discuss only the second Law, which asserts..."

11. May 4, 2007

### becko

Feynman doesn't state that the first law is a special case of the second law.

12. May 5, 2007

### becko

In the modern view, we take the first law as the definition of inertial frames of reference. But, why not take the second? We could define an inertial frame of reference as a frame in which the second law holds. The difference is that the first law says something that the second law doesn't say. See my post here:

13. May 5, 2007

### YellowTaxi

I agree 100% with Feynman, the first law should actually be called Galileo's law of motion, not Newton's.

Newton's second law just looks at what is actually going on when an object DOES speed up or slow down. It just applies some fancy caculus to the first law really and pukes out a useful result.
ie that the acceleration is inversely proprtional to the object's mass.

Last edited: May 5, 2007
14. May 6, 2007

### lpfr

Newton Laws are not enigmas given to men by Gods and subject to interpretations by prophets, priests or physicist.
The meaning of these laws is the one given by Newton himself and no other one. There is not such thing as "modern view" of these laws, no more than Freudian or Hegelian view.

Yes. This is how things have been done for some centuries. The Newton Second Laws works in inertial frames, and, an inertial frame is a frame where Newton Second Laws works.

Yes, I did read your post and this is why a posted a Feynman citation.

If I see a particle whose position or speed is a non differentiable function of time and/or discontinuous, I won't conclude that I am in a non-inertial frame. I will conclude that I leaved the physical world and that I am inside a scene of a science-fiction film as "Stars War". In non-quantum physics all position and speed functions are continuous and differentiable.
And this comes not from the First Law which do not quantify things, but from the second: a discontinuous value of speed or position will ask for an infinite force and we know that this is physically impossible.

First Law is a particular case of Second Law put there for historical reasons.

15. May 8, 2007

### becko

Intuitively it is clear that a force cannot be "infinite" or "not-defined". This comes from our own conceptual ideas of the word "force". Also, we are pretty sure that we cannot move instantaneously from one place to another. But none of this is explicitly stated in Newton's Second Law. All I'm saying is that if the first law weren't there, then, in order to deal with this specific situation, we would have to use our intuition to tell us these evident facts.

I'm not saying that intuition is a bad thing. I'm just saying that it is safer to rely on what is explicitly stated on Newton's Laws and use the facts provided by intuition only when it is necessary. So I still think that Newton's First Law tells us something that is not told by the Second Law.

16. May 8, 2007

### becko

I haven't read any of Newton's books or writings, so correct me if I'm wrong. From what I know, Newton doesn't say that the first law defines inertial frames of reference where the other two laws hold. At least he did not state it that way. Yet, this is the generalized understanding of Newton's Laws in the present time.

When someone writes something, we read it once and make our effort to understand what he meant. After some time, we may read again what he wrote, and it is likely that our understanding of what was meant will improve. This happens because our knowledge is constantly growing and so our interpretations of what we read or hear change too. Also, there is the problem of translation and the gap of time between Newton and ourselves. We cannot claim that our interpretations of Newton's Laws have not changed since the time when they were stated for the first time. Also, Newton himself was not perfect and during the centuries, his laws could have suffered small improvements, which are not too big as to merit the creation of a whole new theory and thus continue to be called Newton's Laws of Motion.

It is true that the "meaning of these laws is the one given by Newton himself and no other one", but how can we be so sure that we understand the right meaning?

17. May 8, 2007

### Ian

Hyacynth,
If you read through Principia you will find that Newton knew he was the first person to express his ideas on mechanics through both quantative and qualitative reasoning. The first Law is qualitative, it is a basic statement. His second law is quantative, it is the mathematical relation of the first.
However, it is not the mathematical relation that is important. What our common sense and logic tell us about the behaviour of systems is what opens doors for us, not the math, math is just a spanner out of the physicists toolbox.
We cannot discard the logic and use only the math, else the math becomes redundant. But you can discard the math and continue the logic. Always keep the first law, it is a fountain.

18. May 9, 2007

### lpfr

As far as I know, Newton only worked with inertial frames and, of course he did not use the terms inertial or non inertial. I'm not 100% sure, but I think that non inertial frames are a much more recent invention. Maybe as recent as 19th century.
As Newton did not consider and ignored the non-inertial frames, there is no possibility that he could have included a hidden meaning in his Laws. He meant what he said and no more.
In theory you do not need non-inertial frames. You can calculate all things from inertial ones. Of course there are a lot of problems easier to calculate and to understand when viewed from non-inertial frames and this is the reason why they where introduced.

" how can we be so sure that we understand the right meaning?
The superiority of Newton Laws, when compared to other non scientific laws, is that he does no limited himself to enounce the laws. He used them to explain many things and to predict others. The "user manual" for his laws and their meaning is his Principia.

As for the need of the first Law, you must not forget that at the time, there where not too many people able to understand a differential formula. Maybe the only other scientific that was capable was Leibniz, who was inventing simultaneously with Newton, the differential calculus. First law was understandable by all scientific people, second no.

I think that, as Feynman did in his Lectures, you must enounce the first Law, out of respect for a genius, and work with the second.

19. May 9, 2007

### explain

The second law is the most useful for calculations, but the other two laws are needed conceptually. Here is an interpretation of Newton's laws:

First law: There exist "objects not acted upon by outside forces", i.e. isolated bodies very far from all other bodies. Also, there exist reference frames in which all isolated bodies move with zero acceleration. Not a separate reference frame for each body, but one reference frame for all such bodies. Henceforth, we consider such reference frames only.

Second law: In a situation when bodies interact, they interact through "forces". Forces are auxiliary vectors for which we have known formulas on a case by case basis (e.g. force of gravitation is inversely proportional to the distance; force of friction is proportional to the normal force; force of viscous friction is proportional to the velocity; force due to magnetic field is given by the Lorentz formula; etc.). In principle, all the forces acting on a body can be identified and computed, then one can compute the second derivative of the position of a body, multiply by the mass, and the result will be equal to the sum of all the forces acting upon the body.

Note: force is not merely "defined" as mass times acceleration. Forces are defined separately, through "force laws", i.e. formulas that need to be specified for each physical interaction, on a case by case basis. Acceleration is also defined separately. Many people like to say that the second law is merely the definition of force, but IMHO it's not useful to think in this way.

Third law: In an isolated system, the sum of all forces is zero. It follows that the total vector of momentum is conserved. This is an asserted property of all the force formulas. In other words, the third law says that we are not ever going to consider force formulas that violate this rule.

20. May 9, 2007

### smallphi

The First Law not only postulates the existence of inertial frames but also defines the 'correct' time parameter in such frames.

If you have a free body (not acted by forces) observed in such a frame, its velocity = change in displacement / change in time parameter. The First law postulates that if you calculate the velocity with a 'good clock' the velocity of the free body will remain a constant. On the other hand if you take a 'bad clock' that at times speeds up or slows down with respect to the 'good clocks', and you calculate the velocity of the free body using the time increments of the 'bad clock', it will look like this velocity varies with time. That will simply reflect the variations of the 'bad clock' with respect to the 'good clocks'.

So in essence the First law shows you how to construct a 'good clock' in inertial frames. Simply take a free body, mark equal distances along its path and define the unit of time as the time for the body to cover one such distance.

I've come to my current understanding after reading an explanation in James Hartle's GR textbook. The same definition of 'good clock' remains locally valid in GR.

Last edited: May 9, 2007
21. May 10, 2007

### ObsessiveMathsFreak

Newton's first law is NOT obvious. Intuitively, we feel that a force or push is necessary to keep an object in motion. We feel that a sliding block will eventually stop unless you keep pushing it. In reality, there is a frictional force that resists motion, which is fooling our senses, so our intuition is wrong.

In the modern world we can come up with examples of objects in outer space, which is a very good setting to begin talking about newton's laws. Many people are familiar with images and animations of objects moving in outers space, though the physics of science fiction isn't always very correct. Nevertheless, appealing to people's intuition about objects in space is I think the best place to start.

So imagine an abject floating in space. Now imagine a situation where we have Newton's second law, but not the first. If we exert a force on the object, it will accelerate in the same direction as the force. However, is it possible to that the object will accelerate or decelerate without a force being exerted on it?

Before Gailileo, and for a while afterwards, people thought that the answer to this was "yes". They thought that an object traveling in space with a fixed velocity would tend to slow down, without any force being applied at all. They knew that objects would accelerate in the direction of forces applied, but thought that objects would decelerate without a force.

In other words, they had Newton's second law, but not the first. The first law isn't a special case of the second. It is separate. They are logically distinct. To descend into mathematical logic here. The second law states that the momentum change is parallel and proportional to the applied force.

Second Law.
$$F\neq 0 \Rightarrow \frac{dP}{dt} = kF$$

But the second law only speaks about applied forces. It does not say what happens when no forces are applied. We need the first law to which states.

First Law.
$$F=0 \Rightarrow \frac{dP}{dt} = 0$$

The logic only goes one way. $$A \RightArrow B$$ does not necessarily mean that $$B \RightArrow A$$. So we cannot infer the first law from the second. It may seem like a subtle point, but it is important, otherwsie objects may be able to change their momentum in the absence of forces.

For course, we can just combine the two laws into one by saying that
$$\forall F \Rightarrow \frac{dP}{dt} = kF$$
Which is what we do mathematically anyway.

But remember, without the first law, it's logically valid for objects to decellerate or even change their direction completely in the absence of applied forces. Objects in space could randomly fly off at right angles if there were no forces about. We need the first law to make our logical system complete.

22. May 13, 2007

### Da-Force

The second law does not state the equation... Newton's second law also states conservation of momentum, and gravitational forces. It REALLY isn't F=ma.. It states that the motion of a mass is accelerated by a force.

Motion can be defined as the momentum (p=mv). or you can have F=ma...