Building equations from the physics


In your previous science classes, when you used math to describe a physical situation you might have been given the equation to use, or it might have been obvious that there was one relevant equation that would suffice. But in less elementary situations, a scientist often has to look at a physical situation and decide how to describe it mathematically. Often, the situation requires applying multiple principles and generating multiple equations. This is a valuable skill for a scientist to develop although it is rarely taught in introductory math classes.  

If you are used to using equations one at a time, this can be tricky. If you look at your situation as a way to "find the equation and calculate something" multiple times, you will be out of luck on many problems. The trick is to name everything you don't know but might need and write all the equations. Bringing in the tools Telling the story and Anchor equations -- Reading the physics in an equation is very valuable here.

Here's a possible path:

  • Give symbol names to all relevant quantities.
  • Find basic principles (equations) that might apply.
  • Construct all relevant equations. Use symbols wherever possible.
  • Specify what symbols are variables and what are parameters. (This depends on the problem!)
  • Decide what we know (given) and what we need to find.
  • Do we have enough equations? If so, solve! If not, look for a missing principle!

To see how we do this, go through the example (from the topic of kinematics) in the Follow-on.

Joe Redish 7/17/17


Article 295
Last Modified: May 27, 2019