“LOL diagrams are my life.” —Honors Physics student from 2010
When I first encountered energy bar charts, or “LOL diagrams” as they’re affectionately known, I wasn’t immediately convinced. Having learned energy problem-solving through traditional methods, these diagrams seemed like an unnecessary, even silly, step. The name “LOL diagrams” itself felt dismissive, highlighting what I perceived as a frivolous approach.
However, my initial skepticism quickly dissolved when I introduced LOL diagrams to my students. I was genuinely surprised by how effectively they helped students structure their thinking around core energy concepts: energy storage, energy transfer, and the principle of energy conservation. The following year, I integrated them into my Honors Physics classes, and the response was overwhelmingly positive. Students who had previously struggled with energy problems, especially more complex ones like calorimetry, found them surprisingly straightforward when approached with LOL diagrams. Where previous classes had found these topics challenging, the LOL diagram approach made them almost trivial. I became a convert.
What are LOL diagrams?
Let’s walk through the initial LOL diagrams we introduce in class. We typically start with a problem and revisit it in several variations to solidify understanding. Here’s the first scenario we explore:
A car on a frictionless roller coaster track, launched by a large spring, successfully completes a loop.
With each LOL diagram, we practice translating the visual representation into a conservation of energy equation. Building on the previous diagram, we then add the equation:
Next, we modify the problem by placing the spring outside of our defined system. This introduces the concept of energy transfer into the system from an external source, which we define as “work.”
Let’s consider a different snapshot in time. Keeping the initial state the same (spring compressed, cart stationary), we now examine the cart when it’s only halfway up the loop. This allows us to compare how energy distribution changes at different points in the system.
These examples provide a foundational understanding of LOL diagrams.
Essentially, LOL diagrams are visual tools to represent energy storage within a chosen system at different moments in time, and to illustrate any changes in the total system energy. Each “L” in “LOL” represents a snapshot in time, showing how energy is stored at that instant. The “O” in the middle defines the system boundaries, indicating which objects are included within the system and which are external. If an object outside the system interacts with it, causing energy transfer (through work, heat, or radiation, although radiation is less common in introductory physics), it’s depicted outside the “O” with an arrow indicating the direction of energy flow and labeled with the type of interaction (e.g., spring force (Fs) in the examples). While we initially focus on qualitative problems to build familiarity with LOL diagrams, labeling the interaction type from the beginning is beneficial for future problem-solving.
The name “LOL diagram” comes from the visual shape of the diagram itself. Students often find the name memorable and engaging, which, combined with their problem-solving utility, makes them a popular tool for grasping the energy transfer model. Even I, initially resistant to the name, have come to appreciate it.
Another advantage of LOL diagrams is their extensibility. They can represent multiple snapshots in a single diagram (e.g., LOLLLLL, LOLOLLL), with additional “O”s only needed if the system’s total energy changes between snapshots.
Consider this example: An object launched upwards by a compressed spring. We can analyze snapshots at three key points in its trajectory.
Conservation of energy equations can then be derived from any pair of these snapshots (L’s) for quantitative problem-solving.
The following sections outline best practices for effectively using LOL diagrams with high school physics students, incorporating refinements developed over several years of teaching.
Quali-Quantitative Approach: Blocks and Triangles
Initially, I used bar heights to represent qualitative energy amounts in my diagrams. While I understood and implemented this, I noticed students struggled to replicate this level of nuance consistently. Their LOL diagrams often appeared “unbalanced,” even when energy wasn’t being transferred across system boundaries. Achieving precise qualitative drawings proved challenging for them.
To address this, I shifted to using blocks to represent energy units. This block-based approach made it immediately clear whether a diagram was intended to be “balanced” or “unbalanced,” as blocks are easily countable.
For clarity, I recommend using half-blocks represented as triangles (as seen in some earlier diagrams). This eliminates ambiguity about whether a block is intentionally shorter or simply imprecisely drawn.
The “x” marked on the axis signifies “zero energy of that type,” indicating a deliberate consideration of energy forms present or absent in the system. This prevents diagrams from appearing incomplete.
Regarding the blocks themselves, it’s crucial not to assign them a fixed numerical energy value. For instance, 3 blocks of kinetic energy (K) and 1 block of gravitational potential energy (Ug) don’t necessarily imply kinetic energy is exactly three times greater than gravitational potential energy. Students can become overly focused on quantitative precision too early, hindering the diagram’s primary purpose as a conceptual tool. Ideally, students should be able to construct a complete LOL diagram before engaging with numerical calculations. Prematurely focusing on quantitative accuracy often leads students to draw diagrams after solving the problem numerically, negating the diagram’s value as a problem-solving aid.
The key insight is that only the change in energy storage for each energy type is crucial when using LOL diagrams.
Therefore, LOL diagrams are fundamentally qualitative, as blocks don’t represent fixed energy quantities. However, they are also quantitative in the sense that the total number of blocks in each snapshot is significant. An increase in total blocks from one snapshot to the next indicates energy entering the system, a decrease signifies energy leaving, and a constant total block count signifies energy conservation within the system.
Practice Writing the Conservation Equation
My experience shows that students significantly benefit from writing a comprehensive conservation of energy equation directly from their LOL diagrams. This “One Big Conservation Equation” approach helps them solve problems by plugging in known values, rather than getting bogged down in numerous smaller calculations using individual energy formulas. It promotes organized thinking and prevents students from losing sight of the overall energy relationships amidst algebraic manipulations.
Starting this year, I’ve incorporated equation writing practice for all qualitative LOL diagrams, even in Honors Physics. The initial results are promising. The real test will be its effectiveness with regular physics classes, which we’ll assess after spring break. Last year, retroactively introducing this equation-writing practice halfway through the energy unit, when students were struggling, yielded substantial improvements.
Graphing Work: A Visual Approach
Calculating work exclusively through graphical methods, rather than equations (we currently omit work equations entirely in Honors Physics), emerged from two pedagogical goals: 1) emphasizing graphical solutions whenever possible and 2) fostering a deeper understanding of the implications of including a spring within the system. This aims to prevent the common student error of calculating spring work using Fs*∆x with only initial or final Fs values.
This graphical approach has been remarkably successful. Students seem to grasp the underlying concepts more thoroughly, and the spring-work misconception has largely disappeared.
Here’s an example of student work illustrating an LOL diagram alongside a graph used to calculate work. While the arrow label is missing in this snippet, the overall approach is sound.
Model Correctly: Consistency is Key
My final piece of advice is to always model LOL diagrams accurately and completely, incorporating every detail you expect students to include. Initially, this was challenging for me as I had internalized a more streamlined mental approach. However, students tend to emulate the diagrams they observe from their teacher. If you omit steps, they are likely to do the same, potentially leading to gaps in their understanding and difficulties in solving energy problems—often mirroring the struggles they might face with equation-only approaches. While your expertise allows for shortcuts, students benefit from seeing the full, detailed process modeled consistently.
Therefore, I recommend these consistent modeling practices:
- ALWAYS define the system first. Do this before drawing any energy bars.
- ALWAYS label work arrows with the object exerting the force on the system. This clarifies the interaction causing energy transfer.
- ALWAYS draw the LOL diagram before writing equations. This prioritizes visual conceptualization.
The most demanding aspect of problem-solving should be constructing an accurate and relevant LOL diagram. Translating the diagram into an equation should be relatively straightforward. Conversely, attempting to write equations without a diagram, or with a hastily drawn, incomplete one, is as challenging as creating a good diagram but with added complexities: abstract symbols, potential sign errors, and a lack of visual structure. Load the physics understanding into the diagram, and let the algebra follow naturally.
