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How does Newton’s second law relate force to the rate of change of momentum?

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Title page of Isaac Newton's Philosophiae Naturalis Principia Mathematica, 1687, featuring large Latin text and publication details in a bordered layout. — Newton’s laws of motion The title page of Isaac Newton's *Philosophiae Naturalis Principia Mathematica* (1687; *Mathematical Principles of Natural Philosophy*), the work in which the physicist introduced his three laws of motion.

In Newton’s second law of motion, the relationship between force and momentum is fundamental: the time rate of change of a body's momentum is equal in both magnitude and direction to the net force applied to it.123

Momentum is defined as the product of a body's mass and its velocity. Because momentum is a vector quantity, a force can alter the magnitude of the momentum, its direction, or both. For a body with constant mass, this relationship is commonly expressed by the equation $F = m a$ , where $F$ is the force, $m$ is the mass, and $a$ is the acceleration (the rate of change of velocity).2314

This law serves as a quantitative description of how forces produce changes in motion, establishing that if a net force acts on a body, it will accelerate, and conversely, if a body is not accelerating, there is no net force acting upon it.24