# Conservation of Momentum in a Single Direction

1. Jan 12, 2014

### JSGandora

The Law of Conservation of Momentum states that the total linear momentum does not change in any closed system not subject to external forces. However, is it true that the momentum in, say, the x-direction does not change in any closed system not subject to forces in the y-direction?

I feel that it is indeed true since y-directional forces do not change the x-directional velocity, thus conserving momentum in the x-direction.

2. Jan 12, 2014

### tiny-tim

Hi JSGandora!
(you mean "not subject to forces in the x-direction")

Yes.

Conservation of momentum comes from the vector equation change of momentum = ∑ external forces.

Since this is a vector equation, you can take components in any direction, and if the component of ∑ external forces in that direction is 0, then the change of momentum in that direction is also 0.

3. Jan 12, 2014

### oneplusone

It does get a bit confusing. Think about a bowling pin at rest, and when you throw a ball at it (at a slight angle) the ball hits the pin, and they both fly off in the xy plane. So before the collision, the momentum in the x direction is whatever the mass of the ball is times the velocity. In the y direction, it's zero.
But after the collision, both objects move in the y direction…how does that work out? Well, consider the vector equations. The mass times the speed of the object moving "upwards" cancels out with the mass time sthe speed of the object moving "downwards".
Remember that momentum is a vector quantity since it's mass times Velocity.

P.S. are you from aops? :)