Impulse

Definition

The impulse due to a force applied over a period of time is the integral of the force over the period of time. In other words, the impulse due to a force $\bar{F} (t)$ (a vector quantity) from time $t = t_{1}$ to time $t = t_{2}$ is given by

$\int_{t_{1}}^{t_{2}} \bar{F} (t) d t$

Impulse is responsible for a change in the linear momentum, and the net impulse on a system equals, as a vector, the change in the linear momentum of the system. This is one of the many formulations of Newton's second law.

The concept of impulse is particularly useful for collisions, where a very large and quickly changing quantity of force is exerted by the two bodies on each other over a very short interval of time. Measuring the force as a function of time is hard, but the total value of the impulse can both be measured and theoretically predicted.

Units and dimensions

The $M L T$ dimensions of impulse are $M L T^{- 1}$ , and the SI units are $k g m / s$ (kilogram meters per second).