It’s late September.
Exam 1 is here already – shit.
You have 4 other courses to study for, and every additional minute spent on Physics is a minute lost for your English 101 paper, your rote memorization of atomic structures for Chem, and for your History of Rock and Roll “test.”
Okay let’s be honest – that last one you squeezed in on the walk across campus to the exam room…
But what if there were a way to shortcut the whole thing, and jump right to the meat: solving difficult problems?
What we’re taught to do
How frustrating can it be to spend hours in lecture, and hours reading textbook chapters, only to feel like you still have no idea how to do the homework problems?
Ever wondered why it happens this way?
Or have we all just assumed this type of struggle is just “part of the process” for those unfortunate souls with a degree program that requires general physics?
Ahhhh, what the life of a business major must be like…
A typical student’s approach
Let’s say you just came out of a lecture introducing Centripetal Acceleration.
The professor shows a rock spinning around attached to the end of a rope (presumably attached to the hand of a small child goofing off in the back yard), and explains that there must be an accelerating force keeping that rock moving in a circle, and preventing it from flying into your neighbor’s window.
(Granted: no kid has actually done something like this since ~1960, but our prof. seems to be slowly losing the battle to father time, so we’ll let it slide.)
We’ve seen stuff like this before, and the textbook does much the same.
(Photo: Knight’s Physics for Scientists and Engineers)
“It’s due to an inward force that doesn’t contribute to the energy of the object, and is always perpendicular to it’s path of travel,” the book says.
On your 4th attempt at re-reading that, hoping to somehow make sense of it by stuffing more of the words into your tired brain, you realize that you have no clue what that means or what to do with it.
What we should actually be doing
Let’s take instead, what I call the Reverse Learning Technique – a tactic you can use to dramatically increase your ability to solve difficult physics problems, without spending hours reading over your notes and textbook examples.
We’re all familiar with reverse engineering – peeling back the layers from a finished product to try to gain insights into the structure, process, and technology that underlies it.
A young engineer at work, taking apart a 1970s VCR. (Photo: Steve Jurvetson)
Reverse Learning works in much the same way. It’s a technique for working backwards from the solution to a complex homework problem or potential test question to a set of related core concepts (lecture and textbooks work the opposite way).
Sticking with our Centripetal Acceleration concept, let’s take a somewhat complex roller-coaster problem as an example.
The Reverse Learning Technique
Suppose you work through an example problem with the TA in your discussion in which you need to find the acceleration vector of the roller coaster cart when it has completed the first quarter of the loop shown below.
This is a somewhat unfamiliar problem that you may not recognize requires a fairly deep understanding of Centripetal Acceleration. Thankfully, you’ve diligently copied down the solution and have it in front of you.
On the down side, it looks a bit like gibberish.
Seriously TA, you couldn’t have thrown in a label or two?
Anyways, you have the solution in front of you: the acceleration is 43.20 m/s2 to the left, and 9.81 m/s2 downwards. And not only that, you have most of the math leading up to it.
Good. This is our Reverse Learning starting point. Now we start asking why.
Let’s start with the obvious one (if you’ve had basic physics), why is there an acceleration downwards of 9.81 m/s2?
Well that’s gravity. As long as the Earth is down, which in this case we are assuming it is, there will always be a downwards acceleration acting on the cart of 9.81 m/s2.
Okay Concept #1 (gravity) down. Now moving right along…
Why is there an acceleration to the left of 43.20 m/s2?
This is a bit trickier, but let’s look at our diagram and see what’s happening to the cart at that point in time.
It’s halfway up the backside of that loop.
And where will it go after that? Up and to the left.
So to keep the cart from flying straight up in the air (like it was shooting off a ramp), there must be something turning that cart to the left as it rises. Well, the only thing there is the track.
Ahh the track – that’s what’s moving the cart to the left.
Okay, so how does the track accelerate something even though it doesn’t itself move?
Well we can ask ourselves: where else does this happen?
Bouncing a tennis ball maybe? The ground provides a reaction force that completely decelerates the ball and changes its direction.
A tennis ball impacting the ground and changing direction. (Photo: Ingrid Taylar)
Oh yeaahh, that’s the Normal Force (reaction force provided by a solid object). That’s why he has that marked as FN on the force diagram.
Great, Concept #2 (Normal Force) down.
So then what’s this equation he wrote using Fn?
Oh wait, that’s showing ac and v2/r. I remember seeing that in lecture.
Right – that’s Centripetal Acceleration, from our diagram before.
And taking that a step further, the answer he gets for the x-direction acceleration (at the end) is the same thing he gets when he calculates Centripetal Acceleration, which as we just saw, is related to the Normal Force.
So the Normal Force must be causing the Centripetal Acceleration, which is moving the cart up and to the left!
Now you’ve related concept #3 (Centripetal Acceleration) – the one we care about in this context – to a concept you already have familiarity with, concept #2 Normal Force.
And you also know that both (1) acceleration due to Gravity and (2) Centripetal Acceleration can interact at the same time on one object, independent of one another.
These are the big insights you need to be able to solve general physics exam problems.
Look at the ground we’ve covered with just a few of the most obvious questions we can ask ourselves about this problem. And there’s still 75% of the work involved in the problem that we haven’t tried to explain yet.
Do you see how this is different than what we’re taught to do?
We’re taught to first, learn the concept. Learn the logic behind everything from someone who already has a deep understanding of the topic. Then, and only then, should you go try to apply it.
Well it turns out this is not too effective. This is not how we naturally learn. And because of that, it makes learning technical material overly difficult. Tough college courses become frustrating, and we lose motivation.
“Just by reading we all think we’ve actually learnt the stuff, but its a whole different story when we try to apply it. I think it just takes some special kind of thinking around the problems that is what makes Physics so hard.”
Comments like this one from /r/PhysicsStudents on reddit are all too common.
There is tremendous insight to be gained by following this internal dialogue type process, and this is much much deeper learning than you would ever achieve by staring at your lecture notes and textbook diagrams.
Work your way through the toughest problems you can get your hands on in this way, and your “physics intuition” and understanding of how different concepts relate will get stronger. You’ll develop the ability to look at a problem, and recall what phenomena are acting, and therefore how to apply a core set of formulas.
And hey, guess what? This is how it works in the real world!!
Trial by fire.
Learn as you go.
Companies don’t have textbooks explaining how to do your job.
You have to figure it out. So might as well get a jump on it now.
I’ll leave you with this gem from a 19th century Brit, Bishop Mandell Creighton, who honestly I know nothing about but his quote fits:
“The one real object of education is to leave a person in the condition of continually asking questions.”
Stop thinking you should know the answers just because you listened to your professor and read the textbook.
Start asking yourself hard questions, of real problems, that make your brain hurt.
Start today – and wave at your fellow students as you pass them by on homework and exams.
And throw in a few skipped lectures… just for fun.