
The integral of a force over time, representing a change in momentum.Impulse is a fundamental concept in mechanics that quantifies the effect of a force applied over time. It is defined as the integral of force with respect to time, and it directly equals the change in momentum of an object. This relationship is known as the impulse-momentum theorem, and it provides a powerful framework for analyzing collisions, impacts, and any situation where forces act for a brief duration.
The concept of impulse is rooted in the work of Isaac Newton, who formulated the second law of motion in terms of the rate of change of momentum. The explicit formulation of impulse as a distinct quantity developed later, with contributions from figures like Jean le Rond d'Alembert and Leonhard Euler in the 18th century.
When a force acts on an object, it changes the object's momentum. The impulse is the cumulative effect of that force over the time interval it acts. Mathematically, impulse (J) equals the average force multiplied by the time duration, or the integral of force over time. The theorem states that this impulse equals the final momentum minus the initial momentum. This is particularly useful because it allows you to calculate the effect of a force without needing to know the details of how the force varies with time.
Impulse is crucial in engineering design, such as in airbags that extend the time of a collision to reduce the force on occupants, and in sports science to analyze the effectiveness of a kick or throw.
The impulse-momentum theorem is why a glass can survive a fall on a carpet but not on a hard floor: the carpet increases the time over which the momentum changes, reducing the force.






