• The normal force is not always pointed upward. The magnitude of the normal force is always perpendicular to the surface.
  • Another come issue is that if my axis is tilted then gravity is no longer all in the Y-direction. There will be components of gravity now.
  • Also when people translate their FBD into Newton's second law many people will use cosine to find the X component of gravity and sine for the Y. You must always check with your FBD and find the angle and draw a right triangle. Often, with tilted axis, sine goes with the X direction and cosine with Y, but not always. It will always depend on the angle you are given.
  • People want to rotate their FBD so that the acceleration is not along an incline. This makes their gravity off at an angle and not straight down. The FBD should be independent of the coordinate system and should represent the direction of the forces.
  • FBD should have the forces in the actual direction they are applied, not in terms of two components. For visualization, it's fine to put the force in with a solid line then use dotted lines to represent each of the components.
  • In general you want the coordinate system in the direction of acceleration. On occasion, not doing so, can be advantageous if it means you have much fewer forces to break into components. The downside to this is that then the acceleration would have components and it's desirable in the algebra to have one of the directions of acceleration to be zero. Practice will tell you when to not align the coordinate system in the direction of acceleration. Either way, the physics should be independent of the choice of coordinate system.
  • Many people will always want to rotate their axis for a situation where there is an inclined plane present. Although this is often best, there are cases where the direction of the object's acceleration is not along the plane of the incline. Pointing the axis in the direction of the acceleration usually trumps all other motivations for a certain coordinate choice.