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Bringing Physics Formulas to Life

Physics formulas written on a whiteboard /chalkboard

Physics will always be an enormous field of study that continues to grow as we learn more about the Universe. Yet fundamentally, it has a wonderfully simple purpose: to understand and explain how things behave as they do. Whether we are looking at the forces acting on everyday objects or the behaviour of matter and energy, physics gives us a way of describing the world through observation, experiment and mathematics.

Its achievements are remarkable. Our understanding of physics has given us electricity generation, radio, lasers, medical imaging, satellites, computers and space travel. It has allowed us to peer inside atoms and look billions of years into the past by studying light that has travelled across the Universe.

But with such an enormous scope, physics can understandably acquire a reputation for being difficult. This word can sometimes become an obstacle in itself, particularly for a student meeting a new topic and wondering whether they are going to understand it. I would much rather replace difficult with fascinating, as this puts us in a better headspace to begin our journeys. We should also be encouraged by the notion that even the most advanced concepts are built from simpler ideas that can be broken down again and again.

Building physics from smaller ideas

One of the core skills involved in learning physics is knowing where to start. Faced with an equation containing several unfamiliar variables, it is easy to see the whole thing as a single problem to be solved. Breaking it apart changes the task considerably.

What does each variable represent? What happens to one quantity when another increases? Which values remain constant? What would I expect to happen if I doubled one value, or halved another? Questions like these turn an equation from something to be memorised into something to be investigated.

That principle extends across physics. We build our understanding piece by piece and then start making connections between those pieces. Ideas that initially seemed separate begin to fit together, and the broader concept gradually becomes visible.

Albert Einstein captured something of this when he wrote that “the whole of science is nothing more than a refinement of everyday thinking.” I like that idea because physics does not begin with equations. It begins with curiosity about what we observe and an attempt to understand why things happen as they do.

A basic understanding of scientific principles therefore gives us another way to make sense of the world around us. We start to recognise why objects move as they do, how energy is transferred, how waves behave and why matter responds to forces. The equations give us a precise language for describing those relationships, but the understanding behind them is what makes the subject come alive.

Finding different routes to understanding

Students learn in different ways, and individual topics can benefit from different approaches too. Sometimes an explanation is enough to unlock an idea. At other times, a diagram, worked example or practical demonstration makes the same concept far easier to grasp.

Repetition plays an important part because each encounter with an idea provides another opportunity to strengthen it. A worked example might introduce the method, followed by a practice question that requires the student to apply it independently. Changing the numbers or circumstances then tests whether the underlying principle has been understood rather than the original example simply remembered.

Experiment adds something particularly useful. It allows a student to ask, what happens if I change this? That question is fundamental to physics because it shifts attention towards the relationships between variables.

Prediction makes the process even more useful. Before changing a value, the student can decide what they think will happen and why. Comparing that prediction with the result creates a cycle of thought, experiment and observation, and any unexpected outcome becomes an invitation to look again.

I have seen the value of these different approaches many times while teaching GCSE and A level physics. Students who have struggled with a concept can make considerable progress when we find another way into it, and that understanding can provide the foundation they need to go on and achieve the top grades they are aiming for. My About me – Physics tutor page explains a little more about my teaching background and approach.

Seeing what an equation actually does

Equations are beautifully concise. A handful of symbols can describe a relationship that applies again and again, but that concision can make an equation seem rather abstract when you first encounter it. Writing values into a formula and calculating an answer is useful, although it gives you only one view of the relationship.

Imagine instead that you could change one of those values repeatedly and immediately see what happens. Increase it a little, then a lot. Hold one variable steady while changing another. Try an extreme value simply to see what it does.

You can begin to spot patterns surprisingly quickly. A relationship that was previously expressed through symbols starts to become something you can see and explore. The equation remains exactly the same, but you have gained another way of understanding what it describes.

This is the idea behind the interactive physics simulations  I have started developing for my students.

A virtual physics lab

I think of the simulations as a small virtual laboratory. They allow students to alter the variables involved in fundamental physics equations and immediately see the consequences. Depending on the simulation, those results can be shown through movement, changing values, diagrams or graphs.

The important part is the freedom to experiment. There is no need to set up apparatus again or work through a fresh calculation every time a value changes, so it becomes easy to ask one question after another. What happens if I increase the mass? What if the velocity changes? What if I try the same experiment with a very different value?

My Conservation of Momentum – Elastic and Inelastic Collisions simulation, for example, allows students to change the masses and velocities of objects and explore what happens to momentum before and after different types of collision. Instead of seeing conservation of momentum through one worked example, students can create many different collisions and watch the same underlying principle emerge each time.

The Electric and Magnetic Fields simulation explores a very different area of physics. Here, students can investigate how charged particles behave in electric and magnetic fields and observe the effect of changing the conditions. The equations describe the relationships precisely, while the simulation gives those relationships movement and form.

The Stationary Waves: String Fixed at Both Ends simulation shows how stationary wave patterns form on a string. Students can observe nodes and antinodes, explore different harmonics and see the striking symmetry of standing waves in motion rather than simply as a static diagram.

Radioactive decay presents another interesting challenge because the behaviour of an individual nucleus is random, while the behaviour of a large population follows a predictable statistical pattern. In my Radioactive Decay: Half-life simulation, students can watch individual nuclei decay and see the resulting decay curve develop. Half-life then becomes something they can observe and measure rather than simply a definition to be learnt.

More experiments to come

These are the beginnings of something I am excited to continue developing. Physics contains so many relationships that lend themselves to this type of exploration. I plan to add further simulations over the coming months. Each one will provide another opportunity for students to experiment with a concept and investigate what happens when its variables change.

I see these simulations as one tool among many. Reading, listening, calculating, drawing diagrams, answering questions, carrying out experiments and revisiting topics all contribute to understanding in different ways. Combining those approaches can be particularly useful when a concept has stubbornly refused to click.

Finding your way into physics

Physics will always require sustained effort. There are mathematical techniques to practise, equations to become familiar with and ideas that take time to absorb. That challenge is also part of what makes the subject so rewarding.

The important thing is to keep finding ways into a topic. Break it into smaller pieces, work through examples, repeat the process, draw it, calculate it, experiment with it and look at what happens when something changes. Each approach adds another piece to the picture, until the relationships beneath the formulas begin to reveal themselves.

That is what I hope my interactive physics simulations can help students to do. Physics becomes far more fascinating when the symbols on the page begin to describe something you can see, explore and understand.

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