Education : Students devising and solving their own problems I apologize in advance for the nature of this question. 
I have been thinking lately of methods to increase the quality of my self-study. I have been meaning, but never actually got to, in addition to solving numerous problems in the textbooks, to construct and solve my own problems, based on the material taught in each chapter. 
Would that be helpful, educationally, or would it be a waste of time? Is this practice carried out in general?
 A: I completely disagree with udiboy. I think you should certainly devise your own problems, precisely for the reasons he's stating. As udiboy is saying, textbook problems are made so that there is a solution. But real world problems are not of this kind. Once you'll become a researcher, if that is the path you want to take, but even in other lines of work, you'll come across problems that nobody has solved before you. If you shelter yourself from this kind of problems by sticking to textbook problems, you're going to have a bad time once you enter your professional life.
However, you should keep in mind that trying to find the solution to those problems is not the most important part. The most important part is be busy with the material you have learned to try to master it. Maybe even devise your own methods. At least elaborate plans on how to attack a problem, even if you don't manage to solve them in the end.
There are many ways you could do this. You could specifically look up open problems in physics, these might be very hard though. What I often do is when I have solved some textbook problem, is to see if I can generalize it and solve the more general problem.
For instance, I have been recently redoing the computations to prove that a suspended chain takes the shape of a $\cosh$ function. This is basic Newtonian mechanics and often a textbook problem. But then I try to extend it. What if the density of the chain is not uniform? What if we take a suspended surface instead of a chain? What if I make a very long chain so that we have to work with the universal law of gravitation? Can I solve it with the action principle? With a Hamiltonian? And this way I make a load of new problems which I can tackle and sometimes I solve them, sometimes I don't. But in the process, I learn to master the basic techniques better. I learn what is fundamental and what is idiosyncratic to the problem.
A: Making problems and solving them by yourself defeats the purpose of a good problem. A good problem can only be made by someone who knows what is actually happening in the problem described, i.e. you should know the solution beforehand to make a good problem.
What you could try is picking up problems from your textbook which you have already solved, and analysing it under different situation. For example, you could consider a friction-less surface based problem and solve it considering some finite value of friction. 
The problem with this is that there is no guarantee you will even find an answer. Sometimes, you will feel the need for extra data, or there might be some concept you are unaware of happening with the new problem. And in most of the cases the solution won't come so easily(Loads of dirty equations to solve and stuff). So you would need the help of someone else, which is not really easy when you are self-studying.
And personally, I think that process is very time consuming.
