PROBLEM SOLVING:
TUTORIALS AND TRICKS OF THE TRADE
GENERAL ADVICE:
WHAT AND HOW TO STUDY:
Physics involves a lot of concepts, ideas, and relations between those, which you must understand and know. BUT, unlike most academic courses, learning conceptual information like this is only the first step to what you need to learn in a physics course (it is the first step, i.e. that's what you must start with, but there are many other steps after it!). Learning physics in this course means learning a skill, very much like learning a craft.
This skill is: how to solve physics problems.
Like anything skill-based, it requires practice, over a period of time.
This is why even if you usually get away with cramming for tests (never an advisable strategy for any course!), and somehow usually get away with it, in physics, it won't work. You can't successfully cram for a physics exam any more than you can successfully cram for learning the guitar or for running a 20 miles marathon.
To learn to solve problems, you need to practice solving problems.
WHEN ATTEMPTING HOMEWORK PROBLEMS:
Before you even DREAM of starting on your homework:
- Learn the conceptual material first (i.e. what the lectures are about, the text in your text book), and learn it well.
Any other way you may attempt to do a problem (guessing by comparing the problem you're given to examples in the book or lectures, sponging off buddies, relying on vague memories from the lectures or previous physics courses you had long ago, etc...) will at best be a waste of your time - and likely affect your grade drastically, in a bad way.
Doing homework problems is about putting your knowledge in practice - to do that, you first need the knowledge!
- Study the examples discussed in the lectures. Here study means: understand how the concepts and ideas explained in English during the lecture are translated in mathematical language, and put into practice.
If you have little prior experience with physics, or for whatever reason you struggle to follow these examples, look at the sample problems/examples in the textbook. This means: read the relevant section, then attempt to do the sample problem/example.
When studying a solved problem like these: never look at the solution straight away. Attempt to find the answer yourself, no matter how off you feel you are going to be. Take a guess, even if it's just a vague, confused one. Even if you're completely wrong, to just really think about the question will help you understand the solution much better.
All this means that you need to give yourself enough time to learn the conceptual material and study the examples before you even start working on the homework, so you must plan accordingly.
Ok, so now you're ready to start with homework.
So you start reading what the first problem wants from you. If you've done physics before I'm sure you've already realized this. If not, stand warned: you're in for experiencing a feeling of confusion! No there's nothing wrong with you, that's completely normal. It will never completely go away, either, but with practice you'll just get used to it! ;-)
We call them "problems" for a reason: you're not expected to know the answer, you're expected to figure it out. There is a wide gap between knowing the information you need to know to solve a problem, and being able to use it. And that's a skill, that you're going to have to develop.
If you've never done physics before especially, the gap may be so wide that you have no idea how to bridge it, for some problems at least. Then definitely go over similar-looking sample problems from the text book first.
Generally speaking: approach problems with the same attitude you'd approach any game. Enjoy the challenge, all of it: the stress of being faced with it, the excitement at the thought you might actually succeed, just maybe, and when you do, the high to win!
Have FUN!!!
This too requires PLANNING, ironically: if you start on your homework just before it's due, there's no way you're ever going to find it fun...
LEARN THE LANGUAGE!
That means:
- use symbols (i.e. letters), not numbers.
- know the meaning of the symbols (ex: a stands for acceleration, and understand what acceleration means).
- many symbols are letters from the greek alphabet. Learn them, don't confuse them with similar looking letters from our (latin) alphabet!
- use subscripts! Yes, really. Most situations will involve the same type of physical quantity (ex: acceleration) for different objects, or/and at different times, or/and different directions. They're all accelerations, but they're not the same one! You need to be able to tell them apart, and to do this you must use subscripts. Sometimes you will not to use two different subscripts (say, one to distinguish which object, and the other what moment in time you are talking about). Sometimes, what subscripts to use will be given in the text of the problem, but most often, you'll need to make them up yourself.
WORKING WITH OTHER STUDENTS:
That can be very useful, but it can also be very dangerous.
For the conceptual material: discuss together what you don't understand well, or you're not sure how well you understand it! That much is very useful without being dangerous ;-)
For the problems: only discuss together what you are stuck on, or unsure about, after really, really trying to solve the problem yourself!
NEVER work on a problem together from the start: you need to develop the ability to go from "Gosh I'm so confused, I don't even know how to start this thing" to "Ok, well perhaps if I try this I'll get somewhere." (Don't panic, I'm exaggerating a little. Only a little though). There is no way you, as an individual, will ever develop this skill if you do this step as a group. And at the exam, you'll be on your own. Don't bank on stress to perform miracles!
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Below is a very general overview of mechanics.
Use the links at the bottom of each section to access material relative to the relevant part of the course.
[The links are a work in progress!]
KINEMATICS:
Involves the description of an object's motion (i.e.movement), in terms of position, distance, velocity, acceleration, usually as functions of time.
Does not involve forces, nor energy and momentum.
Comes in several guises:
- linear motion, i.e. motion through space, in one direction only (i.e. one "dimension")
- linear motion, i.e. motion through space, in two "dimensions" (or three).
- rotational motion: motion about an "axis of rotation", i.e. object spinning on itself, or around some point outside itself.
Link to kinematics problem solving advice/tricks.
DYNAMICS:
Involves forces and/or torques.
Requires to find out what type of forces act on the object of interest.
Problems usually involve applying Newton's second law. This law relates the forces felt by an object to how this object moves as a result - more precisely, to how this object accelerates as a result.
Comes in several guises:
- linear motion, i.e. motion through space (or standing still in space). In this cases the quantities of interest are forces (and linear acceleration).
- rotational motion, i.e. motion about an "axis of rotation", i.e. object spinning on itself, or around some point outside itself.In this cases the quantities of interest are torques (and rotational acceleration).
Link to dynamics problem solving advice/tricks.
CONSERVATION LAWS:
In the context of mechanics, i.e. this semester, these involve two different physical quantities: energy and momentum.
That one of these quantities is conserved for an object or group of objects (either are called the "system"), means that this system has the same total amount of this quantity at all moments of time, this quantity does not change in time, it remains the same.
Conservation of momentum:
- linear motion, in one direction only (i.e. one "dimension")
- linear motion, in two "dimensions" (or three).
- rotational motion: - about an "axis of rotation", i.e. object spinning on itself, or around some point outside itself.
Conservation of energy:
- linear motion .
- rotational motion: about an "axis of rotation", i.e. object spinning on itself, or around some point outside itself.
Link to conservation laws problem solving advice/tricks.
