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When drawing a free body diagram of banking of road, why don't we resolve weight of car into its cos and sin components? It is seen that only normal reaction force and frictional force are resolved

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    $\begingroup$ The component is resolved with respect to axes .... As you see , $mg$ lies on the axis , si no resolution was required... $\endgroup$ – Nehal Samee Mar 27 '18 at 5:25
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    $\begingroup$ @NehalSamee Oh yes right. That point escaped my mind. Thank you. $\endgroup$ – user187749 Mar 27 '18 at 5:27
  • $\begingroup$ @NehalSamee That looks like it should be an answer $\endgroup$ – David Z Mar 27 '18 at 5:38
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Although the choice of axes is arbitrary in lots of cases, including this one, there is a choice which makes solution of a problem easier.

In this problem you want a car to go around a corner without moving up or down vertically.

So one of the axes is chosen to be vertically upward so that the sum of the resolved forces in that direction is zero and the is no motion in the vertical direct and the other axis is chosen to be horizontally inwards so that the sum of the resolved forces in that direction provide the centripetal acceleration to enable the car to turn the corner.

With that choice of axes you have to resolve the frictional force and the normal reaction into two components but the weight of the car only has one component in the vertically down direction.

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