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h1. Coordinate System

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A set of mathematical axes which serve as a quantitative map grid, allowing precise specification of positions of objects.  Cartesian coordinates are most common in introductory mechanics, but cylindrical coordinates are sometimes useful, especially for circular or orbital motion.
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h3. Setting Up Coordinate Systems

h4. Problems Involving Motion

* Sketch an x-axis (and, if needed, a y-axis).
* Clearly specify which direction is positive.
* Clearly specify where you are choosing to place the origin.

h4. Problems Involving Dynamics or Momentum

* Only the orientation of the x (and possibly y) axes need be shown.  The precise origin is usually not important.

{excerpt}h4. Problems Involving Energy

* For problems involving (near-earth) [gravitational|gravity (near-earth)] potential energy it is assumed that up is the positive direction for height.  You must, however, specify a zero-point for the height.
* For problems involving springs, it will be assumed the origin is placed at the equilibrium position of the spring, unless otherwise specified.
* For problems involving (near-earth) gravitational potential energy _and_ springs, you must clearly describe the relationship between the coordinate used in the gravitational potential energy and the coordinate used in the spring potential energy.

h4. Problems Involving Rotation

* Clearly specify the rotation axis.
* Specify the direction of positive rotations about the axis, particularly if you are taking clockwise to be positive.

{note}Graders always appreciate clarity, so specifically indicating that up is positive in a problem involving gravity or that counterclockwise is positive in a problem involving rotation is never considered "overkill".{note}



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