Breaking component of centripetal force [closed]

Question

I recently learned that we always break components of force along and perp to direction of net acceleration (for simplification) So in problems involving circular motion.... We resolve forces along centripetal acc So in problems involving vertical circular motion...we break mg along centrifugal force(ofc working from non inertial frame)

But in problems involving banking of road w friction....we break centrifugal force along and perp to mg ...Why so??

We should have broken Normal and friction along centrifugal force

Answer 1

While applying Newton's 2nd law we first define the axis, generally where the body is more likely to move we take $x$ axis along that direction and $y$ axis perpendicular to the $x$ axis. Here, also during banking the car is more likely to move along the incline plane direction, that is why the $x$ axis taken along that direction and $y$ axis perpendicular to it, and after that forces are broken along that direction. Well, you can also break forces along your chosen axis and can find acceleration. Separately, for the $x$ axis and $y$ axis and then find the net acceleration using vector sum.