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 $F(t)$ from time $t=t_{1}$ to time $t=t_{2}$ is given by

$\int _{t_{1}}^{t_{2}}F(t)\,dt$

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 $MLT$ dimensions of impulse are $MLT^{-1}$, and the SI units are $kgm/s$ (kilogram meters per second).