The study of momentum and impulse is useful to solve problems of collisions and explosions.
Important quantities are:
In a graphic of force versus time, the area under the curve is numerically equal to the impulse of the force in the relevant time interval.
The total impulse received by an object determines its variation in the amount of movement: $$\vec{I} = \Delta \vec{P}$$ or $$\vec{F}_a \Delta t = m \vec{v} - m \vec{v}_0.$$ This theorem is applicable if:
When the sum of all external forces acting on a system is zero, the total momentum of the system remains unchanged, i.e., the momentum is constant. More precisely, we can formulate this theorem as: for some amount of motion \(\vec{P}_A\) at time \(A\) and a quantity \(\vec{P}_B\) at a later time \(B\), we have: $$\vec{P}_A = \vec{P}_B$$ if $$\sum_i \vec{F}_{i} = \vec{O}.$$
The system of interest could be considered as a particle system when consisting of more than one moving part. In this case the following quantities are important: