Is Newton I independent of Newton II?

[vco]

If Newton II is defined as $\sum F = \dot{p}$ and $p = mv$, why do we consider Newton I as a separate law for cases where $\sum F = 0$? Is Newton I really independent of Newton II?

 

[Michael Price]

If Newton II is defined as $\sum F = \dot{p}$ and $p = mv$, why do we consider Newton I as a separate law for cases where $\sum F = 0$? Is Newton I really independent of Newton II?

Newton's first law is spelt out to repudiate the Aristotelian position that objects will naturally come to rest. With that out the way, Newton's 2nd law explains how they actually behave.

 

[vco]

Newton's first law is spelt out to repudiate the Aristotelian position that objects will naturally come to rest. With that out the way, Newton's 2nd law explains how they actually behave.

So there is no strict reason we couldn't state that there are only 2 laws of motion instead of 3?

 

[Dale]

If Newton II is defined as $\sum F = \dot{p}$ and $p = mv$, why do we consider Newton I as a separate law for cases where $\sum F = 0$? Is Newton I really independent of Newton II?

Often the first law is considered a definition of inertial reference frames and the second law is considered a definition of forces.

 

[vco]

Often the first law is considered a definition of inertial reference frames and the second law is considered a definition of forces.

That makes sense, but I don't see why we couldn't attribute both of these definitions to the second law.

 

[PeroK]

That makes sense, but I don't see why we couldn't attribute both of these definitions to the second law.

The second law only holds in a reference frame where the first law holds.

 

[Dale]

That makes sense, but I don't see why we couldn't attribute both of these definitions to the second law.

Hmm, maybe it is possible, but I don’t see an obvious way (and I haven’t seen anyone do something like that). You need to define an inertial frame (so that acceleration is defined) and force.

For inertial frames we take an isolated object (no interactions) and inertial frames are frames where that object moves in a straight line at a constant speed. That is the first law.

Then for the second law we need an object that is experiencing some force (one or more interactions). To define forces. That is the second law.

To define two things from one scenario/equation seems difficult to me. I am not sure how it could be done.

 

[kent davidge]

I think the second law implies the first, but the converse is not true. For a particle could be obeying a bizarre equation of motion which says that the particle will not accelerate if there's no force.

 

[Dale]

I think the second law implies the first, but the converse is not true.

I don’t know how without an independent definition of either an inertial frame (needed to define acceleration) or force.

 

[Herman Trivilino]

Law I is not a consequence of Law II. In modern parlance Law I is the assertion that all inertial reference frames are equivalent.

 

[sophiecentaur]

@vco Your observation shows that you have been 'thinking about' the subject and it is always worth while looking at Science (and the whole of life, for that matter) from a variety of viewpoints.
Newton needed a statement about Change requiring a Force and the basic Maths of N2 would have been foreign to most people in his time. N1 was necessary in its context.