Changing Coordinate Systems to Make Problems Easier

One day a physicist comes across a perplexed student in the library.

It seems that the student had only learned to place his axes with the positive y axis going up and the positive x axis going to the right.

Unfortunately this system wasn’t working so well with a situation involving pulleys and curved directions.

The physicist decides to help the engineer by telling him that the x-y coordinate system can be changed to better suit the problem at hand, much like polar coordinates can be more convenient than cartesian coordinates.

If an object travels in a curved path he reasons that the x-y coordinate system may also be curved in parts for simplicity.

Gravity may be thought of as positive or negative and up may be considered down.

The physicist also says that simply using common sense to check an answer will often times be effective, for instance if a block is sitting on a wall with no forces it will probably just stay there.

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