How do you calculate the change in momentum of an object?

May 4, 2015

There are two possible ways depending on the problem.

1) The change in momentum of an object is its mass times the change in its velocity. $\setminus \Delta p = m \cdot \left(\setminus \Delta v\right) = m \cdot \left({v}_{f} - {v}_{i}\right)$.

${v}_{f}$ and ${v}_{i}$ are the final and initial velocities. Remember to use the right signs when substituting ${v}_{f}$ and ${v}_{i}$

Example) A 3kg mass initially moving 4m/s to the right rebounds off of a wall and begins travelling to the left at 2m/s.

Taking "right" to be the positive direction: ${v}_{i}$=+4m/s, ${v}_{f}$= –2m/s, and m=3kg. Substituting,
\Delta p=3kg*(-2m/s$- 4$m/s)$= - 18$ kg m/s

2) The change in the momentum of an object can also be found by considering the force acting on it. If a force, $F$, acts on an object for a time, $\setminus \Delta t$, the change in the objects momentum is $\setminus \Delta p = F \cdot \setminus \Delta t$.
Remember to use the right sign when substituting $F$. For example, a force to the left could be negative.

Lastly, if your object is moving both horizontally and vertically then $\setminus \Delta p$ has a vertical and horizontal component. If this is the case, the above equations still work for each component separately, Ex) To find the horizontal component of $\setminus \Delta p$ use the horizontal component of ${v}_{i} , {v}_{f}$ or $F$ in the above equations.