# First Newton's Law

1. Dec 15, 2008

### DaTario

Hi All,

This point was raised by a professor friend of mine, in an examination for entering MsC on science education.

Why three laws for mechanics if the first law (inertia) can be derived as a particular case of the second (F = ma) ?
We should have only two laws.

Thak you All,

Sincerely

DaTario

2. Dec 15, 2008

### olgranpappy

In Newton's time it was thought that to "keep an object going" required a force. Newton's first law was an explicit statement that this is not so.

If we state Newton's second law as
$$\sum F =ma$$
then Newton's first law is implicitly included in the 2nd law.

3. Dec 15, 2008

### Andrew Mason

The first law was not Newton's. It was Galileo's. So there are historical reasons for the two laws.

The first law establishes the concept that a body does not change its motion unless acted on by a force. The second law quantifies how the body's motion changes with the applied force. So the second law serves a different purpose.

Also note: Newton did not write "F=ma". He did not use the terms "mass" or "acceleration". The second law refers to "alteration of motion" not "acceleration". Mass is not explicitly discussed at all. See: http://members.tripod.com/~gravitee/axioms.htm" [Broken] (cancel the password request)

AM

Last edited by a moderator: May 3, 2017
4. Dec 16, 2008

This is because first law defines the frame in which 2nd law works. And that frame is inertial frame of reference. There are different ways (all equivalent) of defining an inertial frame. One way is to say that inertial frame is the one in which Newton's first law is applicable. So, given a frame, if you have found whether it is inertial or not, you can check whether to apply 2nd law or not.

5. Dec 16, 2008

### flatmaster

Sure, the first law is a specific case of the second law. However, is it our mission to minimize the number of laws? The first law is the simplest case of the second law. It's helps aid in the understanding of the concept of what a force is. Is it redudnent? Yes. Should it be droped? No; it aids in understanding the concept of a force.

6. Dec 17, 2008

### DaTario

I agree that redundancy has low prority than clearity. But usually any mathematical structure has the tradition of presenting its base, its axiomatical base in a minimal form. Take for example, Peanos, five axioms, Euclid's set, Quantum Mechanics' postulates.

Sincerely

DaTario

7. Dec 17, 2008

### LURCH

Although those terms are never used (and were probably never explicitly thought of at the time), the two laws address inertial and non-inertial frames; two very different conditions.

8. Dec 18, 2008

### DaTario

Could you please elaborate a little more on this?

Thanks

DaTario

9. Dec 18, 2008

### cmos

What Newton called "the quantity of motion," we today call momentum. By today's notation, "the alteration of motion," would be written as dp/dt. From which ma follows for a body with constant mass. This is why F=ma is commonly called Newton's second law; but more generally it is F=dp/dt as originally stated.

Last edited by a moderator: May 3, 2017