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Physics Lessons Review Links Solutions Physics Shop

Proof of Conservation of Momentum in 2D

If you take measurements of mass and velocity of objects before a collision and after a collision, then you can proceed to proving that momentum is conserved in 2 dimensional collisions (collisions in a plane).  We have two different methods for showing (proving) conservation of momentum in a collision.  Both methods take approximately the same amount of time to use.  Simply choose the method which makes the most sense to you.  You should actually become familiar with both methods so you can make an informed decision on which method works for you.

In the following demonstrations of how to prove momentum is conserved, the collision being examined is that of two asteroids colliding in the absence of both air and gravity. (shown below)

asteroid collision animation

Scaled - Measured Vector Method This method involves using a ruler and protractor to create vectors drawn to scale and then measuring the resulting vectors to determine if the two are equal. 
(math skills: multiplication and division)
Trigonometry Method This method involves using trig functions (sin, cos, or tan) to break vectors down into their X and Y components (parts) to see if the totals match before and after the collision.
(math skills: multiplication, division, addition, subtraction, trig functions,)