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- Homework Statement
- Knowing whether there is a "correct" way to approach breaking down vectors by decomposing the normal force compared to the weight.

- Relevant Equations
- F = ma ; W = mg

Good afternoon everyone,

I have a question on Newton's 2nd Law regarding objects on a generic incline. Take for example, a car on a banked curve:

Here in the picture I've provided, you can see that the normal force has been decomposed into the x and y components via sine and cosine of the angle multiplied by N.

My question is.. is there a particular reason that seems to be the norm? When I was an undergraduate, I seemed to always be under the impression that the normal was strictly perpendicular to a surface, and instead, it was the weight vector that was decomposed with the coordinate system parallel to the tilted surface, like this:

My initial thought was that these were equivalent ways of approaching the same idea. Just wanted to be sure.

I have a question on Newton's 2nd Law regarding objects on a generic incline. Take for example, a car on a banked curve:

My question is.. is there a particular reason that seems to be the norm? When I was an undergraduate, I seemed to always be under the impression that the normal was strictly perpendicular to a surface, and instead, it was the weight vector that was decomposed with the coordinate system parallel to the tilted surface, like this: