Law of Conservation of Momentum

Momentum (p) is defined to be the mass of an object multiplied by it's velocity.

The units of measure for momentum are the same as it compoment parts:



The Law of Conservation of Momentum is (as the name suggests, it is a LAW afterall) a very important concept in physics.

Generally speaking, the Law states that when objects collide or otherwise interact, the momentum of the first object combined with the momentum of the second object BEFORE the collision, are equal to the momentum of both objects AFTER the collision:

m1v1i + m2v2i = m1v1f + m2v2f

m1 = mass of the first object

v1 = velocity of the first object

m2 = mass of the second object

v2 = velocity of the second object

and the subscript "i" indicates initial (before the collision/interaction) and the subscript "f" indicates "final" (after the collision/interaction)


Since our class is an introductory course, we'll adopt a fairly basic approach to collsions. That is by way of saying we'll always discuss objects colliding head on and then bouncing directly backwards away from each other. Also, we won't worry about things like energy lost to sound or heat or similar sorts of concerns.

It should be obvious that if we define (as we usually do) positive motion to the right, or up or in the positive x or positive y directions, and negative motion to the left, or down or in the negative x or negative y directions, that we need to keep a CAREFUL eye on the directions the objects are moving both before and after the collision.