Banked turns; do we use the x component of normal force or gravity?

[x86]

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.

 

[willem2]

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

 

[x86]

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

Ah, thank you for clearing this up. It is what I thought.

EDIT: Just to add another question. If the normal force is the Y axis, then gravities X component seems to align perfectly with the road, directly parallel

However, if gravity is the Y axis then it doesn't seem like the normal forces X component is perfectly parallel to the road.

Wouldnt something like that matter?