Is Newton's First Law of Motion really necessary?
Most resources, quite sensibly, explain N(I) in terms of bodies with balanced forces acting on them - the body will either stay stationary or move at a constant velocity. N(II) then follows quite nicely by explaining what unbalanced forces make an object do - namely, accelerate in the direction of the unbalanced (resultant) force. F=ma usually makes an appearance after this.
But, you may wonder, if an object has balanced forces acting on it, F = 0 so therefore a = 0 and, hey presto, you've just showed N(I) follows from N(II). So why did Newton bother stating the first law separately?
The short but unhelpful answer is that we can't know what was on Newton's mind at the time. However, here are some reasons I've seen suggested for why he did what he did:
- A historian might argue that Newton was explicitly showing his readers that he was excluding Aristotelian ideas about objects having a natural level or state they they always endeavoured to reach.
- A 21st-century physicist might argue that the first law defines an inertial frame of reference before the second law can define a non-inertial frame.
- A further thought is that N(II) says that all (resultant) Forces cause accelerations but this doesn't exclude the possibility of other things also causing accelerations. So, an object could have zero resultant force on it, but might nevertheless accelerate due to a different cause. Newton is specifically excluding that possibility and thus saying not only that all resultant forces cause acceleration, but that all accelerations must be caused by resultant forces.
- A more subtle point is that F = ma describes the action of a continually acting force F, whereas Newton's second law is set in terms of an impulsive (i.e. short-acting) force. Bernard-Cohen discusses this at more length in his Guide to Newton's Principia (1999).