Starting out in physics and astronomy can seem overwhelming due to the large amount of different topics covered in introductory courses. Sometimes it seems like every week we have a whole new list of equations to use in our homework. In many academic areas memorizing equations, like the Pythagorean theorem, is very useful for problem solving (and I agree, the Pythagorean theorem is one of those we should have burned in our brain if we work with mathematics.) But it turns out that memorizing astrophysics equations isn’t the best use of our limited time and is unnecessary because course instructors often allow equation sheets for exams.
So instead of spending time memorizing physics equations, I found that having fluency in my physics units helped me to solve problems accurately.
A caveat: Nothing is more important than conceptual understanding.
There’s no doubt that the foundation of doing well in any field is to understand its underlying concepts. It seems counterintuitive, but a person can have strong conceptual understanding while also having a weakness in problem solving. So in addition to conceptual understanding, what helps us solve problems?
The hack: Know your units.
In one of my introductory physics courses, the professor stopped himself on the board mid-calculation and muttered, “Wait, no, my units don’t make sense.” He then erased a couple of lines, revised his work and continued. I realized that he was able to quickly catch his error because he was so fluent in the units. I took that lesson and made ‘knowing my units’ an important part of my study habits. This means having fluency in breaking down and combining units to make other units. For example, energy has a unit of Joule [J]. And a Joule is broken down into force (Newton) times distance (meter) with units of [Nm], and furthermore, force [N] breaks down into mass times acceleration [kg m/s2]. So if in my calculation I end up with the units [kg m2/s2], I know I’ve ended with energy [J]. Hopefully the problem was asking for energy. If not, I can now go back and see where I’ve made my error.
This little hack really helped me, and it’s one I always suggest to my students.
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