<Dd> d p → 1 d t + d p → 2 d t = F → 1, 2 + F → 2, 1 = 0 . (\ displaystyle (\ frac (\ mathrm (d) (\ vec (p)) _ (1)) (\ mathrm (d) t)) + (\ frac (\ mathrm (d) (\ vec (p)) _ (2)) (\ mathrm (d) t)) = (\ vec (F)) _ (1, 2) + (\ vec (F)) _ (2, 1) = 0 .) </Dd> <P> Using similar arguments, this can be generalized to a system with an arbitrary number of particles . In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained . </P> <P> In the special theory of relativity, mass and energy are equivalent (as can be seen by calculating the work required to accelerate an object). When an object's velocity increases, so does its energy and hence its mass equivalent (inertia). It thus requires more force to accelerate it the same amount than it did at a lower velocity . Newton's Second Law </P> <Dl> <Dd> F → = d p → d t (\ displaystyle (\ vec (F)) = (\ frac (\ mathrm (d) (\ vec (p))) (\ mathrm (d) t))) </Dd> </Dl>

Define unit of force using second law of motion