Is Newton I independent of Newton II?

In summary: 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.
  • #1

vco

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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?
 
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  • #2
vco said:
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.
 
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  • #3
Michael Price said:
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?
 
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  • #4
vco said:
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.
 
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  • #5
Dale said:
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.
 
  • #6
vco said:
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.
 
  • #7
vco said:
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.
 
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  • #8
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.
 
  • #9
kent davidge said:
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.
 
  • #10
Law I is not a consequence of Law II. In modern parlance Law I is the assertion that all inertial reference frames are equivalent.
 
  • #11
@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.
 
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1. Is Newton's first law independent of Newton's second law?

Yes, Newton's first law and second law are two independent principles of classical mechanics that describe the motion of objects. They are not dependent on each other and can be applied separately to different situations.

2. What is Newton's first law of motion?

Newton's first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. This is also known as the law of inertia.

3. What is Newton's second law of motion?

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be written as the formula F=ma, where F is force, m is mass, and a is acceleration.

4. How are Newton's first and second laws related?

While they are two separate laws, they are related in that Newton's first law can be seen as a special case of his second law. When there is no net force acting on an object (F=0), the acceleration will also be 0, meaning the object will remain at rest or in uniform motion.

5. Are Newton's laws still valid today?

Yes, Newton's laws of motion are still valid and widely used in modern physics and engineering. They are considered fundamental principles of classical mechanics and have been extensively tested and supported by evidence.

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