I am confused on what the correct way to do this is. In my old physics textbooks

Question

I am confused on what the correct way to do this is. In my old physics textbooks, they say that the x component of gravity is responsible for the centripetal force. However, on the internet and for more advanced topics they say it is the x component of normal force that is responsible for the centripetal force. Analyzing this myself, it seems like it does not matter which method is used, as long as you pick a specific viewpoint and stick to it. Does this hold true? Or is one of them more correct than the other? Thanks.

Explanation / Answer

It depends on your frame of reference. In a frame of reference with a vertical y-axis, gravity is vertical and has no x component, while the road is not horizontal, so the normal force has an x component.

In a frame of reference with an y axis normal to the road, the normal force doesn't have an x component, but gravity does

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