What I Wish I'd Known As A Beginning Physics Student

Experienced physics students always do the same thing whenever they write down an answer to a question: check the units. If the units are wrong, you know you've made a mistake! That way, you can catch your own errors and elevate your grade.

About physics help room videos:
These are intro-level physics videos aimed at students taking their first physics classes. In each video, I'll teach you the fundamentals of a particular physics topic you're likely to meet in your first classes on mechanics and electromagnetism.

About me:

[pietergeerkens]

My High School Physics teacher was superb - and began hammering this into all students from the very first lecture in Grade Eleven. All of us arrived in university three years later (back when Ontario high schools were all five year programs) to find ourselves miles ahead of students from other high schools.

[guyedwards]

Another very helpful tip in more advanced courses: if you derive an equation of motion for your system, double check that it satisfies the boundary conditions, and try to imagine the trajectory your equation describes as time progresses. A lot of the time, if the equation's behavior does not match how you know the system will behave in reality, you've made a mistake

[ChrisSpecker]

When I was a TA, I used to stress that students keep writing the units at every step in their calculations. Too many of them only showed units in the initial setup and the final answer, and didn't catch mistakes that should have been easy to spot.

Some rules to remember:

1) Exponents *never* have units. If you're keeping track of units throughout your calculations and you find a number with units as an exponent, you've left a constant or conversion factor out.

2) You should only add or subtract numbers from each other when they both have the same units. The obvious example for this is when you cut 5 cm off the end of a 5m long pole. It's intuitively obvious that what's left of the pole is neither 1m nor 1 cm long, and one term or the other needs to be multiplied a unit conversion factor before calculating the difference. It's less obvious when you're deep into calculations with many different variables and constants (as in thermodynamics), and keeping track of units along the way helps you catch when you've accidentally left one of them out.

[douglasstrother]

This touches on a technique called Dimensional Analysis which determines the allowed functional form of a dependent variable in terms of independent variables by imposing consistency of units on each side of the equation.

[Flatunello]

When I studied physics in the 60s and then 70s in college (I now own an engineering firm), we always carried units through the calculations, even when using calculators (In the 60s, I used a slide rule). In my first engineering mechanics class, we studied Buckingham-Pi, where dimensional analysis is a necessity to analyze complex phenomena.

[wwdh]

Fun fact: My mentor used dimensional analysis to show that you cannot specify the torque constant (newton-meters per ampere) and back EMF (volts per radian per second) of a DC motor independently: those two parameters have the same units! So DC motors function equally well as DC generators.

[wwdh]

Ah yes, dimensional analysis!
I like using MathCAD to solve engineering problems because it does a good job of carrying units through calculations.
At the end of a calculation, you can specify the units to be displayed for the result, such as meters in the example in the video.
Then if the result is not just a number times the units you specified, but has extra unit factors (seconds, coulombs, etc.), you made a mistake.

[charleshudson]

Can't tell you how many times as a physics student I depended on dimensional analysis, step by step, to guide me to the correct solution. (BTW: The negative solutions of quadratic equations, which we normally ignore for being 'unreal' in the everyday world, possess, mathematically, intriguing symmetries in Alice in Wonderland-like 'mirror' worlds. As a former physics teacher, I always liked to show students what the negative solution to a quadratic implies. A rotation. A reflection. Etc. Because, in the quantum realm, you can't ignore an 'unreal' solution - as Dirac proved in his eponymous equation: antimatter. I found students liked a bit of imaginative magic from time to time.) Wish I had your videos back in my student days. (But, back then - before quarks and the Standard Model - there were no videos, no YouTube, no Internet, no handheld calculators; just pencil, paper and slide rule.)

[MrOvipare]

After a few seconds in the video, I thought "UNITS!"
I agree 100%, this is the single most useful little trick that I too wish I used since the beggining.

[hernandezdiazjuanpablo]

Keep doing videos like this bro, they are awesome!

[noelschwabenland]

Great video, could you share some tips with higher level of physics? Im really struggling with theoretical physics, maybe you have some general advice

[TIOS]

Keep it up, excellent. I have to say, I know and use this technique but it’s quite important. They say even Einstein checked his dimensions and if dimensions across the equals sign and in all additive terms didn’t match, he knew he’d done something incorrect.

[Pgan]

The hardest part in Physics are the Calculations. How to be good at this? Is there a Formula to Solve All Physics Problems, like Theory of Everything Equations?

[jamaalbuki]

Just came across your channel and instantly subbed. We need more creators like you, who explain physics intuitively while making it fun. Keep on posting, your going to go viral soon.

[RAFAELSILVA-bydy]

I find a lot of students simply plug and chug with the numbers, so they never get an equation to check. They have a page of numerical calculations and end up with something like x = 17.51349742 m. That seems to be the way physics is often taught.

You can also to some extent check the sines and cosines by trying theta = 0 and theta = 90 degrees and checking whether what comes out looks sensible for a horizontal or vertical initial trajectory.

[ElCidPhysics]

Unit analysis was thought from the very beginning of my physics studies. Yet so many people fail to do that.

[derekapolloalambatin]

I can see this Channel would skyrocket.

[josemanuelperezzegarra]

This year I began college and I received my firtst F exam (0 out of ten). The thing is that the exam wasn't that wrong. I asked my techer and he sais: This is the typical exam where the student does not take care of dimensions. Although the procedure to obtain those equations was right, the result was inconsistent, so I should have payed attention to the dimensions.
Lesson learned xD

[bradleygaddis]

Excellent explanation. But the music is very distracting. Creates a windchime effect!

[declanwk]

when I was first introduced to dimensional analysis, my teacher used a clumsy square bracket notation, which put me off. The method presented here, using the units, is much quicker and more intuitive to use.