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

1 Answer
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. #\Delta p=m*(\Deltav)=m*(v_f-v_i)#.

#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*(-2#m/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, #\Delta t#, the change in the objects momentum is #\Delta p= F*\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 #\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 #\Delta p# use the horizontal component of #v_i, v_f# or #F# in the above equations.