impulsemomentum

Impulsemomentum is a fundamental concept in physics describing the relation between the force applied to an object over time and the resulting change in its motion. The impulse-momentum theorem states that the impulse J delivered to an object equals the change in its momentum p: J = Δp = p_f − p_i. Impulse is the time integral of force: J = ∫ F dt, and momentum is p = m v. For a body of constant mass, this reduces to J = m(v_f − v_i). Momentum has units of kg·m/s and impulse has units of N·s, making the two quantities directly comparable.

The theorem is widely used to analyze collisions, impacts, and propulsion. In a collision, the average force during contact times the contact duration yields the change in velocity, given the mass. It also underpins braking calculations in vehicles, ballistics, and sports, where a short, large force causes a large velocity change, and a longer, smaller force yields a smaller Δv.

For systems with changing mass, the relation J = Δp remains valid for the system as a whole, although interpretation requires considering the total momentum of the system rather than a single mass. The impulse-momentum principle is a direct consequence of Newton's second law and provides a practical framework for predicting motion under time-varying forces.