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Newtons 2nd Law of Motion
The second law states that the net force on an object is equal to the rate of change (that is, the derivative) of its linear momentum pin an inertial reference frame:
The second law can also be stated in terms of an object's acceleration. Since the law is valid only for constant-mass systems, the mass can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus,
where F is the net force applied, m is the mass of the body, and a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it.
Consistent with the first law, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude; such is the case with uniform circular motion. The relationship also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum.
Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (seebelow).
Newton's second law requires modification if the effects of special relativity are to be taken into account, because at high speeds the approximation that momentum is the product of rest mass and velocity is not accurate.
Isang tao, munting taong kaharia’y nasa bukid,
May maliit na bakurang abot-tanaw ng silahis;
Nagtatanod – isang kubong kabahaya’y tila langit;
Ang libangan, halamanang sa looba’y nagtatalik;
Sa maghapon, ang kawaksi’y ang…...