The book says that:

Newton’s first law does not say what happens for an object with zero net force, that is, multiple forces that cancel; it says what happens in the absence of external forces.

So, If an object was moving at constant velocity, and then two forces with net force zero acted on it, will it accelerate(and not obey Newton's First Law)?

  • $\begingroup$ -Physics for Scientists and Engineers with Modern Physics; Serway, Jewett; Ninth edition; Page 114 $\endgroup$ – Mason Nov 2 '18 at 20:04
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    $\begingroup$ It could rotate differently. $\endgroup$ – Qmechanic Nov 2 '18 at 20:47
  • $\begingroup$ @Qmechanic It is moving at constant velocity, how would it rotate then? $\endgroup$ – Mason Nov 3 '18 at 8:51
  • $\begingroup$ With zero net force there could still be a non-zero torque. $\endgroup$ – Qmechanic Nov 3 '18 at 9:31

The answer to this question is surprisingly subtle. If multiple forces that add up to zero act on an object, then it does not accelerate. (Although the object experiences angular acceleration if it's spatially extended and the forces produce a nonzero net torque.)

But the reason that its velocity remain constant is not because of Newton's first law - it's because of Newton's second law, which describes how an object behaves under the influence of external forces. While you would get the right answer by naively applying Newton's first law to this situation, it's logically incorrect to do so. That's because the first law is not simply a special case of the second law, as it's often presented to be. Instead, it acts as a definition of inertial frames.

The second law is not a generalization of the first law - when stated precisely, it doesn't make any sense without the first law. That's because talking about forces netting out to zero - or even corresponding to vectors at all - actually implicitly assumes a whole lot of nontrivial empirical results that are contained within the second law when it's stated in full. I discuss those subtleties here.

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If the net force adds up to zero, then the object should adhere to Newton's First and it's motion should be the same as if there were no external forces acting on the system.

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  • $\begingroup$ don't forget the possible torque $\endgroup$ – Wolphram jonny Nov 3 '18 at 4:05

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