Unlike most people who study physics, I was not naturally good at math. In fact, I barely passed most of my math classes in high school and had to take Calculus 1 multiple times as an adult.
However, once I made up my mind that I wanted to learn physics, I worked hard, studied, and figured out how to excel despite being so weak in the math necessary to major in it.
Since I wasn’t a natural at math–let alone physics–I had to figure out how to do well enough to keep up with everything in class. I figured out that there were certain core ideas that I needed to know and make second nature. Once I thoroughly learned these physics concepts, graduating was easy.
This post covers the mindset and skills that you need to gain a firm grasp of introductory physics. But first, I want to cover something that terrifies many students who find out that they have to take a physics class.
Is Physics Hard?
Physics, itself, isn’t hard.
What’s hard is that Physics is the first time that many students actually have to use their knowledge to solve problems as opposed to merely regurgitating facts.
Physics not only forces you to think abstractly also but represent those abstract ideas with concrete mathematics. It’s not difficult to grasp physics concepts. It’s not difficult to solve the math. The challenge is representing the former in terms of the latter AND being able to describe it with the most precise language possible.
There aren’t many things that force us to do this so we just don’t have a lot of practice doing it. While there are some people who are naturally a little better with numbers, I don’t think anyone just knows algebra or physics.
This might seem obvious, but the implications of it aren’t. People tend to forget that physics is like anything else: it’s only difficult while you don’t know much. Once you understand what’s going on, you just have to do the work and before you know it, you’ll know physics.
More than anything, you need to believe that you can actually learn physics. I grew up failing math in high school and took Calculus three different times before it finally clicked. If I can learn physics well enough to get a bachelor’s degree in it, anyone can.
Here is a list of things you must practice and skills you need to develop if you want to give yourself the best chance at learning basic physics.
The Math You Need For Basic Physics
While physics demands that you generally have high numerical literacy, there are some specific mathematical ideas that you will see so often that it’s important that you make sure you master them. The following is a list of the most frequently used math ideas in basic physics.
You should be very comfortable taking the sine, cosine, and tangent of an angle. You’ll need this in both mechanics and electromagnetics. You’ll primarily use this to figure out the sums of force vectors and the angle they point.
In physics, it’s not a simple matter of figuring out how fast or how far an object has traveled. You’ll also need to figure out its trajectory and angle of ascent or descent. Trigonometry is useful here as well when you need to figure out the path an object takes when forces moving in different directions collide.
It’s more accurate to say that you’ll need to use algebraic thinking more than actual algebra in the sense that you’re used to seeing it. Algebra, in the broadest sense, is the branch of mathematics that deals with symbols and rules for manipulating those symbols.
In your physics studies, very often you’ll need to look at one symbol and figure out other ways to represent it with different symbols. Consider the formula for force:
F(force) = M(mass) × A(acceleration)
You can rewrite this two different ways:
F = M × (V÷t); V = velocity, t = time
F = (D × vol) × (V÷t); D = density, vol = volume
This algebraic idea of representing one concept as another is the key to working through many physics problems. Rewriting one symbol as the composite of 2 or more other symbols (and vice-versa) is essential to your success.
I know there are physics classes that you can take without calculus. I’ve never taken one, but I’ve tutored students who have. My experience has been that you are limited in what you can discuss because calculus arms you with the tools to calculate the acceleration of an object at any given point in time.
Instantaneous acceleration is a key idea in studying physics, and you can’t do it if you don’t how to take the derivative of an equation that represents the path an object takes.
However, the real beauty of studying calculus is that it gives you a stronger intuitive grasp of rates of change. Depending on how ambitious you are with physics, you’ll have to learn a lot more than calculus (namely linear algebra, differential equations, and probability).
If you only take Physics 1 or 2, then a decent grasp of calculus–specifically, differential calculus that you learn in level 1–is the highest level you need.
Specifically, you need to understand the concept of a dimension and what it means for any math problems you see.
When we speak of dimensions, we’re describing the number of directions an object can move through space.
2 dimensions: Can move horizontally and vertically. It’s the “area” measurement. Any location can be described with 2 coordinates (x,y).
3 dimensions: Can move vertically, horizontally, and change depth. It’s the “volume” measurement. Any location can be described with 3 coordinates (x,y,z)
4 dimensions: Can move vertically, horizontally, change depth, and move through time. It’s the “space-time” measurement. Any location can be described with 4 coordinates (x,y,z,t).
Most of us, in the course of our physics studies, will never encounter dimensions any higher.
You’ll also need to be able to calculate the area and volume of the basic shapes and know the sum of their internal angle measure. This may seem elementary, but you should not have to waste precious cognitive power working out the angle measures you’re taking the sign of or the area of the object you’re working with.
Physics is the study of matter and energy and how it moves through time and space. This means that every equation you learn and every problem you solve will deal with you making a relationship between space, time, matter, and energy.
Concepts You Need To Know For Basic Physics
Newton’s Laws of Motion
Until you begin studying modern physics concepts (quantum mechanics and Einstein’s theory of special and general relativity), every problem you encounter can be solved with an application of one of Newton’s Three Laws of Motion.
It’s important that you realize this.
Whether it be classical mechanics, sound waves, or electromagnetism, Newton’s Three Laws of Motion will apply to all systems, particles, electric charges, and magnetic fields. The problem may seem complex or the math required may seem difficult, but it always comes down to figuring out how to:
- Balance a force on an object to account for its position or constant speed (Newton’s First Law and Newton’s Third law)
- Unbalance the forces on an object so that it starts moving (Newton’s First Law and Newton’s Second law)
Remember that a force is anything that causes an object to move. Physics is the study of forces in nature. Remembering that nothing in the physical world is exempt from Newton’s Three Laws of Motion and that will help you feel comfortable in solving problems.
Conservation of Energy
The other key concept you’ll most frequently encounter is the conservation of energy.
Officially, this is the First Law of Thermodynamics and it states that “energy can neither be created nor destroyed; energy can only be transferred or changed from one form to another.”
In other words, what you start with is what you have to end with.
While this isn’t the most precise version of the law (no conversion is 100% efficient, leading to loss as heat), it’s useful enough to make predictions and do calculations. Most students in introductory physics or Physics 1 and 2 won’t be expected to factor in heat loss.
Many of the problems you encounter will deal with the total energy of a system. The total energy of a system is the sum of its kinetic and potential energy. If you lose some potential energy in the system, you gain some kinetic energy and vice-vice versa, but the total energy is constant.
When dealing with collisions, this same idea is often expressed as the conservation of mass. The math differs slightly, but the main idea is that when you deal with a system and any changes that happen to it over time–assuming nothing is added or taken away–the total energy remains constant.
How To Study Basic Physics
Know the definitions of physics terms and be precise in your wording
Do you understand the difference between speed and velocity or current and voltage? What about the difference between area and volume or momentum and force? Or the difference between pitch and volume or displacement and distance?
These are words that are used interchangeably in colloquial speech, but they have a very specific meaning in physics. These are just examples, but you can get into a lot of trouble if you don’t know exactly what these mean. While physics is a math-heavy discipline, you need to be able to accurately describe the problem before you can solve it.
Many of the issues that students face are because they simply aren’t sure what a term means. In physics, you have to be absolutely certain you know what all words in the problem mean, otherwise, you increase your chances of getting the incorrect solution.
Be able to describe things in your own words
Albert Einstein once famously said, “If you can’t explain it simply, you don’t understand it well enough.” Nowhere is this more true than in physics.
Students who have trouble with physics tend to approach the subject as something that they can just memorize and regurgitate. As a result, they never take the time to really understand what’s going on. When this student attempts to define any physics phenomena, they sound like they’re reading directly from a textbook or dictionary.
They can recall the words, but they have no idea what they mean. I often noticed this when I began tutoring physics. Richard Feynman described this as “fragile knowledge”.
Fragile knowledge occurs when a person can understand something in a textbook setting, but they’re unable to apply it to anything in the real world. When students have fragile knowledge, they can’t effectively use what they’ve learned. For many students, studying physics is the first time they’re unable to rely on memorization and regurgitation.
The students could tell me the exact value of the gravitational constant, but they’d get confused when I asked them what is the acceleration of an object due to gravity. Most students memorize the former “G” = 9.81 m/s-1, but they don’t realize it’s the same thing as the acceleration of an object due to gravity.
A great way to overcome this tendency is to focus on making sure that you can explain something simply. I’d always make my students do this, and if it sounded like they were reading from a textbook, then I wouldn’t accept their explanation.
Know how to express an idea as its mathematical equivalent
Every term in physics can be described by a mathematical formula. This is by design, as physics is a discipline that describes the universe and the only way to do this universally and accurately is with numbers.
You should be able to write a word problem as an equation or create a word problem from an equation. You will be better at solving problems when you can look at the numbers and immediately know the corresponding word (or words) to describe them. Likewise, when you see a word, you should immediately think of the corresponding formula or mathematical representation.
For example, you should immediately look at the word “momentum” and not only see the formula that leads to it, but also catch how it’s different from “force”. The same idea holds for figuring out the difference between “velocity” and “acceleration”. When you can see the math that defines the word, the words no longer seem so similar.
Don’t memorize anything
My optics professor, Dr. Theodore Corcovilos, once told our class, “Don’t use a formula if you can’t derive it.” Despite the fact that most physics programs will allow you to bring a formula sheet to the exam, this was potent advice about the nature of doing physics.
The formulas are just there so you don’t have to waste mental bandwidth memorizing them. Math is the medium that physics is done in, but it’s not the point of the problems. You’re not training to be a mathematician. You’re training to do physics. This means that you need to focus on learning how to do that.
Yes, you need mathematical proficiency, but that’s so you can solve problems and understand the relationships between things. The equations and formulas are just different tools to help you. It’s important that you understand the function of each tool so you don’t perform the mathematical equivalent of using a pair of pliers to tighten a bolt or a jigsaw to chop a piece of wood.
The point of my professor’s idea wasn’t to make sure that we could create a useful equation from scratch. It was so we could understand how to use the equation, what the results from that equation should look like, and realize the limitations of each equation at our disposal.
If you can do all of that, you’ll avoid using the wrong equation, using a complicated equation to solve a simple problem, and other errors that occur when you attempt to merely “plug and chug” your way to victory.
Visualize EVERYTHING and relate it to your experience
Although physics requires a lot of mathematics–so much so that everyone who has a physics degree automatically gets a minor in mathematics–it always models reality. This means that it’s very easy to visualize everything you study in classical physics.
Impulse and circular motion are areas that tend to be challenging until you really take the time to visualize real-world experiences and examples of these forces. This is especially effective if you make the examples personal to you.
The typical case given for a real example of impulse is how an airbag works. That was helpful, but I gained a much deeper understanding of the principle when I thought about how you roll with the punches in boxing to lessen the force you experience.
Physics is unique to the other sciences in that it quantifies the experiences you already have.
You may not fully understand the mathematical differences between velocity and acceleration, but you know that you can walk on a bus when it’s moving a constant speed versus when it’s moving up a hill. You may not know the exact formula for figuring out the coefficient of friction, but you realize that ice is more difficult to run on than asphalt.
If you can’t visualize it, draw it
Everything in physics can be drawn. Because it’s a science that models and describes how matter and energy interact in space and time, this means that you can draw everything you study in classical physics.
Every physics student is taught how to draw free-body diagrams. If you’ve never been taught this, this is a great tutorial on drawing them. These simple diagrams make it easy to visualize the forces at play, but they may be too simplistic for certain people.
I personally enjoyed drawing full boxes of relative scale, springs, and vectors of the appropriate length when I solved many of problems. It doesn’t matter what you prefer. All that matters is that you get into the habit of drawing the problems.
Physics is not something you do in your head. It’s something you experience daily, quantify with numbers, and represent with simple drawings.
A Summary of The How To Study And Learn Basic Physics
- Learn algebra, trigonometry, and calculus.
- Master Newton’s Three Laws of Motion and The First Law of Thermodynamics.
- Know the definitions and mathematical representations of words.
- Be able to explain ideas simply in your own words.
- Don’t memorize anything.
- Visualize things
- Draw what you can’t easily visualize
If you follow these steps, you should have no problem being able to study and learn physics.