Foundational Physics

Short Answer: Momentum is conserved separately in each direction only when the net external impulse in that direction is zero. During a brief collision, an external force can change the horizontal momentum of an object without appreciably changing its vertical momentum—or the reverse. The important question is which forces act on the system you choose.

How Can Momentum Change in Just One Direction?

Imagine a small ball moving diagonally toward a smooth vertical wall. The ball has horizontal motion toward the wall and vertical motion upward.

When the ball strikes the wall, the wall pushes sideways on it. That push reverses the ball’s horizontal velocity. But a smooth, frictionless wall gives essentially no vertical impulse. During a very brief impact, gravity also gives only a small vertical impulse.

The ball’s horizontal momentum changes, while its vertical momentum remains approximately the same. It is the direction of the external impulse—not a special kind of collision—that makes the difference.

What Does “Conserved in One Direction” Actually Mean?

Momentum has direction, so we can examine its horizontal and vertical components separately. For any system, the change in horizontal momentum equals the net external horizontal impulse. The change in vertical momentum equals the net external vertical impulse.

If the horizontal impulse is not zero, horizontal momentum is not conserved for that system. If the vertical impulse is negligible, vertical momentum is approximately conserved during that interval.

This does not mean the ball has constant vertical momentum forever. Gravity continues to change it before and after the collision; the approximation concerns the short impact time.

Why Does Choosing the System Matter?

If our system is just the ball, the wall’s push is an external force. That is why the ball’s horizontal momentum can change.

If we choose a larger system that includes the ball, wall, and Earth, the force between ball and wall is internal. Momentum lost by the ball is transferred to the wall and Earth. For a sufficiently isolated larger system, total momentum is conserved in both directions.

So a statement such as “horizontal momentum is not conserved” must always name whose momentum we are tracking.

Does This Only Happen at a Wall?

No. Think of an object landing on a level floor. During impact, the floor can deliver a large upward impulse while providing almost no sideways impulse if it is smooth. In that brief collision, the object’s vertical momentum changes substantially, while its horizontal momentum stays nearly the same.

Both examples show the same pattern: an external impulse changes momentum in the direction it acts.

The Key Idea to Remember

Check the external impulse separately for each direction. A momentum component is conserved when the net external impulse along that direction is zero. The conclusion depends on the system and the time interval.

When This Breaks

A rough wall can exert friction vertically as well as a normal force horizontally, so both momentum components may change. Gravity’s impulse also matters if the time interval is long enough.

Never assume that momentum is conserved in one direction solely because you drew an x- or y-axis. First identify the system, then check all external impulses along each axis.

Keep Exploring

Continue with the Momentum and Collisions Unit Review.

Choose the course that matches yours, then a review depth that fits your time.

Reviewed by Physics Sensei

Still stuck? Get unstuck. Choose the review that matches your course and the time you have.