What is Force in Newtonian Mechanics & Newton's First Law?

[Aarne]

Is Newton's first law the definition of force in Newtonian mechanics?
If not: 1) What is the definition of force in Newtonian mechanics?
2) What is the purpose of Newton's first law?

 

[ZapperZ]

Is Newton's first law the definition of force in Newtonian mechanics?
If not: 1) What is the definition of force in Newtonian mechanics?
2) What is the purpose of Newton's first law?

Er... Newton's 1st Law is the description of "inertia".

F=ma is Newton's 2nd Law. I would call that a "definition" of force.

Zz.

 

[arildno]

Historically, Newton's first law is Galilei's law of inertia.

Perhaps the most significant idea contained within it, is that it actually refutes the previous notion that steady motion requires a "force" to uphold it.

Even Newton struggled a while with this aristotelian idea, and thought at first, as most others, that a moving body had some "internal" force that kept it moving, in the absence of external forces.

This idea of an ever-present "internal" force in a body impeded him from formulating the 3.law, because such an internal force would violate the idea of forces working in action&reaction couples.

Furthermore, as long as one thought there was some hidden force source in a body, rather than that all the mechanically relevant sources for motion could be found outside it, the idea that one could control&quantify dynamics would seem implausible at the outset.

Newton cut through this Gordian knot by formulating his 3 succinct laws, and established the field of mathematical physics.

 

[Aarne]

Er... Newton's 1st Law is the description of "inertia".

Yes, it does describe inertia(resistance of a physical object to a change in its state of motion or rest), but my reasoning is that Newton's first law says that force<=>acceleration. Is it not the case?

F=ma is Newton's 2nd Law. I would call that a "definition" of force

How so? The book I'm using and all the professors I've consulted say that Newton's 2nd law is the definition of inertial mass.

 

[arildno]

Yes, it does describe inertia(resistance of a physical object to a change in its state of motion or rest), but my reasoning is that Newton's first law says that force<=>acceleration. Is it not the case?

Absolutely not!

Newton's first law is, for example, perfectly consistent with a pseudo-law like "whatever external forces work on an object, the object's acceleration is always zero"

 

[ZapperZ]

Yes, it does describe inertia(resistance of a physical object to a change in its state of motion or rest), but my reasoning is that Newton's first law says that force<=>acceleration. Is it not the case?

The 1st law is a "handwaving" description of the EFFECT of force. But it deals more with describing inertia. Notice that just because you know that force can affect the motion of mass, it doesn't tell you HOW it is affected, i.e. it is only a qualitative description, not quantitative.

How so? The book I'm using and all the professors I've consulted say that Newton's 2nd law is the definition of inertial mass.

It could also be a definition of force, because now, we have a more mathematical connection between "mass" and "force". If you want to use this as a 'definition of mass', go right ahead. It is mathematically valid either way. But at least now, one has a clear definition on how they are related.

Zz.

 

[Dadface]

The second law expresses the first law as a special case i.e. when F=0,a=0.

 

[stevenb]

What is the purpose of Newton's first law?

I've heard it said that the first law can be interpreted as the statement that "inertial frames exist". That appeals to me personally.

 

[quantum123]

Newton's first law is actually a copyright infingement of Galilean relativity.

 

[K^2]

First law defines an inertial system. That is its purpose. If you take a coordinate system in which the first law fails, the second law will not hold either, unless you introduce fictitious forces that fix the first law. Simplest example of this is rotating coordinate system. One has to introduce centrifugal and Coriolis forces for the first law to hold.

 

[DaTario]

It really seems to be a redundant statement if placed near the second law. But we must understand the reasons why he organized his propositions in this way. In some sense it is a matter of preference.

Best wishes,

DaTario