First Newton's Law: Why Only Two?

[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

 

[olgranpappy]

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

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.

 

[Andrew Mason]

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.

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" (cancel the password request)

LAW I.

Every body perseveres 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.

LAW II.

The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

AM

 

[visharad]

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.

 

[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.

 

[DaTario]

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.

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

 

[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.

 

[DaTario]

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.

Could you please elaborate a little more on this?

Thanks

DaTario

 

[cmos]

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" (cancel the password request)

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.