Newton's second law

Newton's second law states that the force applied to a body produces a proportional acceleration; the relationship between the two is

where F is the net force applied, m is the mass of the body, and a is the body's acceleration. If the body is subject to multiple forces at the same time, then the net force is the vector sum of the individual forces:

The second law also states that the net force is equal to the time derivative of the body's momentum p:

where, since the law is valid only for constant-mass systems,^[16][17][18] the mass can be taken inside the differentiation operator by the constant factor rule in differentiation. 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 (see below).

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 (see time derivative). The relationship also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. This can be said easily. Net force is equal to rate of change of momentum for those who are unfamiliar with calculus.

Newton's second law requires modification if the effects of special relativity are to be taken into account, since it is no longer true that momentum is the product of inertial mass and velocity.