Newton's first law says that an object remains at rest or moves at a constant motion if there is no external force. Why do some objects remain at rest, while the others move at constant motion?

  • $\begingroup$ Hey, in my frame of reference the "others" are at rest and "some object" is moving... $\endgroup$ – dmckee Mar 20 '18 at 19:51

Being at rest is a special case of *moving at constant velocity", namely moving at the constant velocity =0. In fact, you could leave out this part of the sentence without losing anything.

Alternatively you could say, that, if there is no force, the object is not accelerated (i.e. acceleration=0).

Just a note:

While Newton's laws are sometimes stated as you did, you need to realize that it is a bit of a lazy shorthand notation of the law. Two things need to be expanded on:

  1. The "force" is actually the total effective force, i.e. the (vector) sum of all external forces. Of course, if you apply two equal in magnitude forces acting in opposite directions, the object would not accelerate either.
  2. It is actually not the velocity that is constant, but the momentum (mass times velocity). Similarly, in the absence of a force, it is actually not the acceleration that is zero, but the time derivative of the momentum. However, this is only of relevance in cases where the mass changes (e.g. in rockets). If the mass is constant, you end up with the simple version of the law (constant velocity, zero acceleration).
  • $\begingroup$ Well... this cleared something I've been searching for months. Can't accept the answer yet though, StackExchange tells me to wait 3 minutes. But I still have one doubt. My book says, in a Tug of War, when both teams pull at the same force, the object remains stationary? Does stationary mean constant acceleration? $\endgroup$ – MythicalCode_ Mar 20 '18 at 12:57
  • $\begingroup$ Stationary means V = 0 and constant. That is no net force is applied to the body and as such a = 0 as well. $\endgroup$ – Alchimista Mar 20 '18 at 13:57
  • $\begingroup$ And the answer to your title question is that if there is not force the momentum mv of the body does not change (rocket like motion apart). Because in ordinary words is weird to say that something move with V = 0. Is the state of motion (the momentum above) that doesn't change. $\endgroup$ – Alchimista Mar 20 '18 at 14:05

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