# 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.

sophiecentaur
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?

Last edited:
Mentor
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.

Michael Price
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.

Homework Helper
Gold Member
2022 Award
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.

Mentor
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.

DaveE
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.

Mentor
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.