What is the expression of Newton's second law in terms of momentum?

Newton's second law in terms of momentum is F = dp/dt: force equals the time rate of change of momentum. More precisely, the equation normally refers to the net external force and is written in vector form as F = d p/dt.

Momentum is defined as p = mv, the product of mass and velocity. If an object's mass remains constant, differentiating this expression gives F = m dv/dt = ma, the familiar form of Newton's second law. The momentum form is more general because it directly tracks changes in both velocity and, when relevant, mass.

The law was rooted in Isaac Newton's 1687 description of force as related to a change in “quantity of motion,” the historical concept corresponding to momentum. Modern calculus expresses that relationship compactly as a derivative. Integrating the equation over time produces impulse: the net impulse equals the object's change in momentum.

F = ma is therefore not a competing answer; it is the constant-mass special case. By contrast, p = mv only defines momentum, while F = Gm₁m₂/r² describes gravitational force between two masses.