Why can friction make observing Newton's first law of motion difficult?
The friction would slow down the moving object, so if you didn't know it slowed down due to friction, then you could assume that there was no outside force slowing it down, so that kind of disproves the law.
Newton's first law is kind of circular. We define the net absence of forces to be the state where an object moves uniformly.
Another way to put that is: Newton's first law says that if there is no (outside) force, an object will continue moving at constant speed. Since there is always friction, there is NEVER "no outside force".
Where did you find this definition? What is meant by "uniformly?"
i think he meant constantly or at rest.
Yes, that's what I meant. Uniformly meant "without acceleration."
I didn't find the definition anywhere. It is my interpretation. Force is most naturally defined though newton's 2nd law (generalization of the 1st law). What other definition would you like?
Based on this, I can see why you think it is a circular definition. I myself had this problem not very long ago (I thought that the definition of "inertial frame" was circular, but I think it might be the same fundamental issue). The good news, at least for me, is that I got the conflict resolved, with the help of sereral contributors (of whom lethe was not the least).
Anyway, here's my resolution:
A rest frame is inertial if you can "connect" a mass to the origin by a massless spring, and the spring will not stretch.
It is a little figurative (not practicable), but the concept is sound, and it serves to eliminate the circularity, because the equilibrium point of the spring is well defined according to its rest length.
Now, Newton's first law says that free particles will move in straight lines with respect to such a frame (assuming space is flat).
We seem to be thinking of different things. I didn't have an issue with the definition of an inertial frame. My internal picture was similar to what you described.
In your statement that I am quoting, I meant that labeling the particle as "free" is defined by its straight-line motion.
This is not true. A free particle is one that moves through a region of constant potential without constraint (since this is Newton's law, we're talking about mechanics in 17th century terms). This itself says nothing of the shape of the trajectory. That's where Newton's first law comes in. Given that there is no potential gradient and no surface onto which the particle is constrained, Newton says that the trajectory of such a particle is straight in an inertial frame and the velocity does not change.
You can't define potentials without talking about how they affect trajectories.
Also, the title of this thread is a force that can't be described by a potential
I'll have to think about this one. Just off the top of my head, I would say that you can, because energy is an abstraction that does not require a trajectory, so the same can be said of a potential, which is closely related to energy (energy/interaction factor). IMO, Newton's first law is how a potential affects a trajectory, and that the definition is just backwards, not circular.
Yes, I agree. I think that would be a good reason why friction makes the first law difficult to observe.
I don't see how this is circular. What if we defined the net absence of forces to be when a body accelerates at 1 m/s2. Would that be circular? In any event, if Newton's first law were a definition, then we could write
No net forces act upon a body if and only if the body moves uniformly.
This is a defintion, so we must use the equivalence. In which case, I see no circular reasoning. However, Newton's first law says,
A body in will move in uniform motion unless acted upon by an external force.
which is equivalent to
If an external force does not act on a body, then the body will move in uniform motion.
which is not an equivalence.
If we then considered a body moving uniformly, and claimed that no external forces acted on the body, we would be using false logic. But the second law is not just a generalization of the first. The second law permits reasoning in the backward direction. It tells us,
A force F acting on a body gives it an acceleration a which is in the direction of the force and has magnitude inversely proportional to the mass m of the body.
Mathematically, a=F/m. This is an equivalence. So if we consider a particle with zero acceleration, we are permitted to conclude that no forces act on it.
I should mention that we have defined acceleration to be a change in velocity. That is, a body does not move uniformly if and only if the body accelerates.
Newton's first law is not a definition, is it?
No it is not, that was part of my point.
Separate names with a comma.