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Momentum transfer

This image shows different possible paths that result in a collision. Intuitively, we know which way the object should continue along the wall. Determining this mathematically is a bit more challenging.


The object could go in one of two directions. That is, it could follow the wall one way or the other. But why should it prefer one direction over another? We need a generalized rule that applies for every wall and every angle of approach.

The rule is that momentum is transferred along the path of least resistance. Least resistance is the difference between the wall angle and the angle of approach that is less than 90 degrees.


This raises the issue that a line's angle is determined by its direction. This means that the end point we start with determines the angle of the line. See the line below. Is it a 45 degree line, or a 225 degree line? It depends on which point you start from. But, for a generalized rule of momentum transfer, the answer shouldn't matter.

Consider an object moving at 75 degrees and colliding with a 45 degree wall (or a 225 degree wall). | 75 - 45 | = 30. We will transfer momentum into a 45 degree path. If we tried | 75 - 225 | we get 150. Since this is more than 90, we subtract 225 - 180 to determine the correct angle, ie. 45 degrees.


This is how to divert momentum into another path for any angle of approach into a wall, regardless of the angles or directions involved.

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