# Anchor equations -- Reading the physics in an equation

#### Prerequisites

A central idea in the use of math in science is that an equation expresses a relationship among physical parameters and variables. This means that the equation is not just a calculational tool. It provides a way of understanding the kinds of quantities being related:

- through dimensional analysis of the equation,
- by exploring the functional dependence of the parameters on each other,
- by picking out special cases that yield insights into what's happening,
- and organizing our conceptual knowledge.

Because of all these valuable properties of some equations for building physical insights, we refer to these equations as ** anchor equations**.

One of the implications of finding an anchor equation is that it can be of real value in organizing your studying of physics for quizzes and exams, and for figuring out ways to get started on a homework problem when you are not sure what to do first. Identifying an anchor equation can help you generate relationships and other equations relative to a particular situation, and it can help you make sense of what's happening in a problem qualitatively.

One way we will help you identify some of the key anchor equations (and you will need to decide for yourself on others that are of value to you!) is through the pages titled "Reading the content in the ....[equation, law, principle]".

Here are a few:

- Reading the content in the kinematic equations
- Reading the content in Newton's 2nd law
- Reading the content in Newton's 3rd law
- Reading the content in the friction equations
- Reading the content in Coulomb's law
- Reading the content in Fick's law
- Reading the content in the Work-Energy theorem
- Reading the content in Bernoulli's principle
- Reading the content in the ideal gas law
- Reading the content in the harmonic oscillator solution
- Reading the content in a sinusoidal wave

Each of the equations on these pages are not only helpful for solving problems by doing calculations, but also for thinking about the physical situation, organizing your knowledge, and solving qualitative problems as well.

Thanks to Khala Marshall-Watkins for suggesting the term anchor equation.

Joe Redish 3/3/19

Last Modified: September 7, 2021