How can we differentiate a statics and dynamics problem? Here is the problem I confused a lot.

A uniform rod of mass m and length l is hanging vertically from the pivot O. A horizontal force F acts at the lower end of the rod. If F always remains horizontal then maximum angular displacement of the rod is______.

First I thought the problem is of statics but later thought that the rod is actually moving so I finally thought it should be dynamics problem. Now I don't know how to approach to this problem. Am I lacking knowledge or am I not intelligent enough.
My only question is how tricky or hard problems are solved by begginers like me because textbooks gives theory and leave us with problems where we either confuse or didn't know the process of solving. Sometimes it feels like demotivating because I didn't see any progress in solving problems after spending a lot of time.
Should I again read the theory or just think what is happening in the problem by imagination. Or should I experiment the problem with real objects and predict the solution methodology (Which I don't know).
I know it is a general question but I really want to know what the textbooks really expecting from students. Please tell how to tackle problems of hard level and process required for achieving that level.
 A: I will offer some general advice on how to handle ambiguity in a question, and how to tackle hard problems.
First, if you think a question is ambiguous, meaning you think the words have more than one legitimate interpretation in terms of what is physically going on and what is being asked, then a correct scientific response is to state clearly, in your answer, that you think there is this ambiguity, and then make clear in your own work what physical problem you will address. If you are pressed for time, then you would probably pick whichever is the simple reading of the problem, or whichever seems to match best to the course content you have followed. But if you have plenty of time then you can answer all versions of the problem! Just make a list and answer them one by one. In the present example a static interpretation is legitimate and simpler, so you should probably answer that way in the first instance. But then you could add that the wording could be construed as allowing a dynamic case, and then you could tackle that. (If you are in an exam with time limits then probably you should not spend too much time on that if you think the static answer has a good chance of being what the question really meant).
As for difficult problems in general, when you are stuck as to how to formulate the problem, there are various tools you should have in your tool-box, including:

*

*draw a clear diagram to help clarify your understanding

*if it is an abstract problem then propose a concrete example

*get some general intuition by deciding what you think will happen approximately, without doing any calculation in the first instance

*construct a simpler problem of the same general kind, and see if you can answer that. This often gives useful pointers for the more complex problem.

*make it crystal clear to yourself what are the known quantities and what are the unknown quantities. Develop the mathematical skill of knowing when you have enough equations to determine the values of all the unknowns.

*Always be clear in your reasoning on the difference between an equation which follows from those before, and a new equation which brings in new information. Do not just write a list of mathematical statements; include the symbol for "implies" and use words such as "now," and "using ..."

*When you have a set of simultaneous equations and you have decided (tool 5) that they are sufficient, then make a clear decision as to what you are going to do next. Often it will be to eliminate one unknown, by combining equations so that it no longer appears.

(Regarding ambiguity, I would like to recount a nice story which I read in a book by Martin Gardner. It concerns a question which asked "How would you use a barometer to measure the height of a tall building?" A clever student gave a whole list of answers, ranging from "dangle it on a rope till it touches the ground then measure the length of the rope and add the height of the barometer" to "take it to the caretaker and offer to give him the barometer if he will tell you the height of the building". Of course the answer the examiner expected was to discuss the air pressure variation with height. A good student would have known this and so would have written that type of answer. It is valuable to note that almost any statement can be interpreted in more than one way, and one aspect of scientific understanding is to have good instincts on how to interpret statements.)
A: This is a statics problem.

About the distinction between statics problems and dynamics problems:
Here is an example of an extremely simple case of a statics problem: you have a bowl, you release a marble at an arbitrary point. The marble rolls down, overshoots, rolls back, etc, etc. After a little while friction has removed all motion. When the marble has come to rest, where has it come to rest?
(Of course, this is ridiculously simple setup, it is this simple for the purpose of explanation.)
The final position of the marble, after friction has removed all velocity, is all the way at the bottom of the bowl.
In statics it isn't necessary to describe how the marble arrived at the final state. In statics it is sufficient to identify what that final state will be.
At the same time: it is actually necessary to describe the properties of the possible motion of the marble in order to formally state the nature of the final state.
When the marble is sitting at the bottom of the bowl then any motion of the marble requires that some work must be done. The final state is a state of lowest potential.
The marble-in-a-bowl case is very simple, but this approach of finding where the potential is lowest is the way to mathematically derive things like the shape of a soap film between two circular pieces of wire

Now to the case you presented in your question.
Imagine that you create that setup, and you make sure there is a moderate amount of friction.
Take the rod to an arbitrary angle, and release it. The rod will swing, but the friction will gradually rob it of its motion. The rod will come to rest at an equilibrium position.
The larger the angle of the rod, the larger the tendency of gravity to draw the rod back to vertical.
And then there is a force F that tends to increase the angle.
So you have to work out how the tendency of gravity to draw the rod back to vertical increases with the angle. That will allow you to identify the equilibrium point.

So you do need to take into account, mathematically, in what way change of position of the rod affects the force balance. Still, to find the answer it does not matter along which trajectory the rod arrives at the final position.

By contrast, it's a dynamics problem when you are asked to describe how an object will proceed over time. If you are asked to give the shape of a trajectory, that is a dynamics problem.
A: This is a dynamics problem. You have to equate the work done by the force $F$ with the energy gained by the rod when it has reached its maximum angular displacement from the vertical. Note that at this point of maximum displacement the angular speed of the rod is zero, so its kinetic energy is also zero.
Although the question does not state that the pivot at O is smooth (frictionless), I think you have to assume this - otherwise you have no way to account for energy lost due to friction at the pivot.
A: Granted the wording isn't very clear of the situation.

*

*Is the force applied gradually and the rod settles at the angle at which all forces balance out $\sum \vec{F} = 0$ after a very long long long time?


*Or is the full force enacted at time zero and the rod starts to swing between the vertical and some other configuration with maximum angle?
Since the problem mentions maximum angle, and not final angle I suppose this is a dynamics problem.
In general, the type of approach (static vs. dynamic) is dictated by what result is sought after.
A: I would base this decision on context.  If the problem is from a section of the course  (or book) dealing with statics, treat it as a statics problem.  Find the angle where the torque produce by the horizontal force balances the torque produced by gravity.  As a dynamics problem you want an angle where the work done by (F) equals the increase in the potential energy of the rod and the K.E. = 0.
A: It's hard to tell what they are asking. But I agree with @R.W. Bird answer that you need the problem in context.
In the absence of context, I would be inclined to treat it as a statics problem as I would interpret "maximum angular displacement" to mean the  maximum possible angular displacement where static equilibrium is possible for a purely horizontal applied force. See the figures below. But I can see it interpreted as being a dynamics problem as in the other answers.
For static equilibrium, the sum of the moments about the pivot point $O$ must equal zero (assumes frictionless pivot). This means the clockwise moment due to the weight about $O$ would have to equal the counterclockwise moment about $O$ due to the horizontally applied force. Then relationship between the applied force $F$ and the angle $\theta$ with the vertical becomes
$$F=\frac{mg\tan\theta}{2}$$
Note that for an angle of 0 deg, the applied force $F$ would need to be zero for rotational equilibrium. As the angle increases, the required force $F$ increases. As the angle approaches 90 degrees, the moment arm of $F$ approaches zero, and the required applied force approaches infinity. At 90 degrees there is no counter-clockwise moment to oppose the clockwise moment due to the weight of the rod, since the line of action of $F$ would be through $O$. The only way rotational equilibrium can be maintained is if $F$ were to no longer be purely horizontal, i.e., if it had an upward vertical component to provide a counter-clockwise moment.
Bottom line: If treated as a statics problem, the maximum angular displacement would have to be less than 90 degrees.
Hope this helps.

A: This is a dynamics problem since the rod is moving but I think the question whether it is a static or dynamic problem isn't really important here.
Now to your actual problem: not understanding problems is sadly an important part of physics and of science in general. Physics can be quite complicated and most things you can't just reason on your own: you have to see a similar problem done or you have to know the theory. So don't be afraid to ask help, either on this site or from your friends or your teachers. How are you supposed to know that you can view this force $\vec F$ as a force similar to gravity so if you add those two together you get a new gravity $\vec {F}{'}_g=\vec F_g+\vec F$ and if you rotate your setup until the new force points down the problem is similar to a pendulum only experiencing gravity starting at some angle $\theta$ and this angle $\theta$ is just the angle between $\vec {F}{'}_g$ and $\vec F_g$? So again it is normal to struggle a bit and even the smartest people have experienced times where they felt dumb or inadequate. But if you're struggling it does mean that you have to put in work to get to a level where you're struggling less. It might take some time though before you notice the effects of your work.
