# A Newton's laws controversy

• posted

We all know the three Newton's laws of motion, i'm interested in the first and second because is my feeling that they're very related, and indeed, i think that the first is a particular case of the second one, but... could that be correct? they're not supposed to be mutually exclusive in order to form a consistent system of laws?

because if the first law is a particular case of the second, it could be easily removed from the fundamental principles of mechanics? doesn't it? what do you think about it?

=)

• posted

I don't think they are even close.

there are two ways to look at it -

A) Newton's laws set the parameters for the artificial concept called force -

1) force's effect on mass 2) force's relationship to mass and acceleration 3)force's creation causing creation of an opposite force.

B)

1st law deals with momentum

m1v1=m2v2

2nd law deals with force elements

f=ma

3rd law deals with forces created by a force f1= -f2, mag f1= mag f2
• posted

There are numerous ways of dealing with Newton's Laws. The ubiquitous introductory text by Halliday and Resnick, Fundamentals of Physics, treats the First Law as a special case of the Second Law in which the net external force is zero, just as you have done. Goldstein, in Classical Dynamics, also gives the Second Law a privileged position.

On the other hand, the widely-used text by Marion and Thornton, Classical Dynamics of Particles and Systems, treats the First and Second Laws as definitions, and the Third Law as the actual physical law.

However, Marion and Thornton also refer to Lindsay and Morgenau's book Foundations of Physics, which they say presents the First and Second Laws as physical laws and the Third Law as a consequence. (I have not looked up this reference, so I don't know how they do it).

Ernst Mach, in his Science of Mechanics, condensed all three laws into one law, which makes no mention of either force or mass. His version goes like this: "When two compact objects act on each other, they accelerate in opposite directions, and the ratio of their accelerations is always the same." It is easy to see that working definitions of force and mass can be derived from this.

Newton's Laws were formulated three centuries ago, and they have been stated in many different ways since then. Which statement is best is clearly a matter of opinion. However they are stated, they seem to provide a good way to deal with problems of non-relativistic motion (although not, by any means, the only way; for certain problems, Lagrangian or Hamiltonian formulations are simpler). Since we are engineers, this is what we really care about: a satisfactory set of equations for solving practical problems.

Dave Palmer

• posted
1. Newton's first law says that a body at rest remains at rest, and that a body in uniform motion continues in that uniform motion unless disturbed. This is basically a statement of conservation of momentum.

1. Newton's second law is the well known F = m a that talks about how momentum is changed.

2. Newton's third law is the statement that every action (force) has an equal and opposite reaction (force).

The originator can make the case that the first law can be derived from the second law with some further development, although the two statement are certainly not equivalent as they stand. Why would we need to remove it? Perhaps to satisfy some ideas about minimum sets of assumptions.

At the time Newton first stated his laws, calculus was new and not widely known. This would have made the development of the first law from the second law not possible for most people (if they did not know the necessary calculus). It does not appear that Newton was concerned with reducing his number of laws to a minimum; he wanted to state the results that he thought were important.

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