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.
@@denischen8196 Not so much a half century ago, when this happened. I can still hear the rich Scottish burr with which he opened each class with "Please open your booooks to page xyz.". R.I.P. "Bookers" Wilson. Thank you.
I double that. I see it from the very beginning of physics, probably, in high school. It is called the unit method. Also, there are advanced techniques using a similar approach. For example, sometimes you can introduce long distances and short distances and attribute different units to them. For example, you can create a problem where the geometry of some optical beams and wavelength work together. You will introduce variables related to wavelengths and variables related to the geometry of the optical setup, and they will never mix together, even though the units are formally the same. So, you can work with them as if they were the values measured in different physical units.
@@denischen8196 Rare? Hm... pretty much all of my colleagues knew the unit method. It is even strange to assume that someone is not familiar with that. Maybe this is one of the reasons they became physicists? 🙂
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.
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
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.
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.
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.
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.
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 RU-vid, no Internet, no handheld calculators; just pencil, paper and slide rule.)
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.
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.
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.
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?
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
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.
The problem of checking units is that exams often have limited time and there is only enough time to solve each problem once. This method is useful when doing lab experiments and writing reports where correctness is far more important than speed because every step in a series of calculations must be correct for the final result to be correct.
Fair point on a timed exam! One suggestion is to think about the units in your head as you work through your solution, so that you catch your mistakes right after you make them. When you get to your final answer and do your unit check, if you find that they came out wrong---but you don't have time to backtrack and fix your mistake---I would write down a comment that you think you must have made a mistake because the units are off. When I grade exams, I always give some points back to students with wrong answers, but who checked their units and indicated they know something's off!
I started wondering about the meaning of the dropped t value which was a negative one! My concluson is that a beautiful and in a sense a symmetrical result developed: imagine that at that negative time point somebody throwed the ball with such a speed and direction that by t=0 the ball would reach height=h and speed=v with theta angle to the horizontal line as described in the original example. At the end we can see from the negative timepoint to the positive one a parabola with the stipluated initial conditions at t=0. A full rainbow type shape.😊
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.
This guy is telling me to check my dimensions and here's me that's already been doing that and somehow ending up with the matching unit for the wrong answer.
Except when you have a normalising constant like the Gravitational, Coulomb or permittivity constant which is just too difficult to remember or confusing to calculate
It's easiest to think about how they show up in an equation you remember. Newton's law F = G Mm/r^2, for example. You want to get Newtons for the force on the left, so to find the units for G you start out with Newtons and then multiply by meters^2 to cancel out the units from r^2, and divide by kg^2 to cancel out the two masses. Then G ~ N m^2/kg^2.
LOL. What a ball of crap. It took three painful years, but I taught myself to write perfect exams in high school - not because I didn't make algebra mistakes, but because I learned how to present my work so that I could catch those mistakes before handing in my paper.
