# The diagram tool

#### Prerequisites

When we are looking at a physical situation and trying to see what is happening — either to tell the story of the physical mechanism or to build an equation to quantify our description — drawing a careful diagram often helps.

Looking at a real world physical system and trying to model it mathematically is often challenging. Whenever we're trying to understand something in the real world, we have to decide what to pay attention to and what to ignore. We'd like to decide what physics principles to apply and what equations to set up. That's often tricky. One good way to start is often to draw a diagram.

In solving a problem, your instructor might ask you to draw a diagram as part of your answer. While sometimes a diagram is an answer to a question, more often your instructor is giving you a hint by asking you to draw a diagram. Diagrams are tools that can help you solve a problem. A good diagram can make visible relationships and patterns in the physical situation that you might not otherwise be able to see.

When you're not sure how to start a problem, often a good first step is to draw a diagram. That's because that act of choosing a diagram forces you to make some modeling decisions. What should I include in my diagram? How simple should it be? How realistic? Sometimes a diagram should be highly schematic, other times it should include factors you think you are going to need. The key into create a diagram that will let you see something about the problem that might have otherwise been hard to see.

Often, when students are asked to draw a diagram they either sloppily sketch something at random or draw something as realistically as they can. Both of those approaches are rarely useful. The care needed in creating a diagram involves deciding what is important in the given problem and drawing your diagram to represent those features sufficiently accurately that you can see them easily.

For example:

• If directions matter, be careful to get your angles approximately correct. If some angle in a triangle is a right angle, that permits you to use trig to set up equations relations the sides. Drawing the triangle sloppily so you can't tell which angle is 90o makes the diagram useless.
• If you are drawing vectors and what matters is balance or which is greater, be careful to draw the vectors so that their lengths are relatively correct. If two vectors add up to equal a third, that should be clear from your diagram.
• Graphs are diagrams too. If you are creating a graph of something, pay attention to salient features. Where does is start? Do you expect the lines to be straight or curved? Where do you expect it to turn around or cross zero? Your graph should make those salient points easy to see and to relate to other points on the graph.

We've chosen as our icon for this tool a compass and protractor (with a straight edge along the bottom). For most diagrams you construct, you won't have to build them that carefully, but they are meant to suggest: straight lines should look like straight lines; acute angles should look like acute angles; and circles or parts of circles should look like circular arcs.

Drawing your diagrams carefully and then looking at them to see what they tell you is a valuable tool to master!

Joe Redish 5/16/19

Article 643