How can I improve my skills in finding general solutions in physics?

[TimeInquirer]

Hello, few days ago I took an exam in my honors physics class and believe I did not do as well as I did on the other exam. Last exam had a few computational problems and the rest were general solution problems. This recent exam had 8 questions that were all general solution problems as opposed to the last exam which only had 4 or so. My question is how can I become better at finding general solutions. My next exam is on the laws of gravitation, shell theorem, and Kepler which are much harder topics than previous ones. Any advice or links geared toward general solution problems in these topics?

 

[PeroK]

Hello, few days ago I took an exam in my honors physics class and believe I did not do as well as I did on the other exam. Last exam had a few computational problems and the rest were general solution problems. This recent exam had 8 questions that were all general solution problems as opposed to the last exam which only had 4 or so. My question is how can I become better at finding general solutions. My next exam is on the laws of gravitation, shell theorem, and Kepler which are much harder topics than previous ones. Any advice or links geared toward general solution problems in these topics?

What do you mean by "general" solutions?

 

[TimeInquirer]

I guess I should have explained that before. Here is an example: An object in the shape of a thin ring has radius Z and mass M. A uniform sphere with mass M1 and radius R is placed with its center at a distance x to the left of the center of the ring, along a line through the center of the ring, and perpendicular to its plane. What is the gravitational force that the sphere exerts on the ring-shaped object?

The type of problems that require you to manipulate and relate equations and variables.

 

[PeroK]

I guess I should have explained that before. Here is an example: An object in the shape of a thin ring has radius Z and mass M. A uniform sphere with mass M1 and radius R is placed with its center at a distance x to the left of the center of the ring, along a line through the center of the ring, and perpendicular to its plane. What is the gravitational force that the sphere exerts on the ring-shaped object?

The type of problems that require you to manipulate and relate equations and variables.

My advice would be to treat all problems as general problems (as far as possible): solve them as generally as possible and then plug in the numbers at the end, if that is required. This should help build an understanding of the physics. Even if you are given mass, velocity and angle etc, don't use the numerical values.

What are the most advanced things you can do in general terms? Are you comfortable with general projectile motion, for example? Or, are you only comfortable plugging numbers into equations?

 

[TimeInquirer]

To be honest, I command of those problems is not where I would like it to be only because I did not take a respectable physics class in high school and jumped into honors in college. My weakness in general solution problems is in springs, circular motion, tension, and pendulum motion. I like your idea about treating all problems as general problems.

In regards to computational problems, I don't have much trouble with them. Just small mistakes such as forgetting the negative or whatever but it rarely happens

 

[PeroK]

I don't have anything systematic, but here are some things I always do:

1) Try to get the physics of the problem sorted out in your head before you use any formulas. That one you quoted is a good example. Try to work out what happens first. Which way will the ring move? Then move on to trying to get an equation for it.

2) Use general variables where possible.

3) When you get a formula, check what happens if you increase/decrease a key variable (e.g. mass). Does the answer change the way you would expect?

4) If you reduce a variable to 0, does the formula reduce to something that you already know. In your example, if the offset x = 0, then the ring and sphere should be in equilibrium.

5) If you get stuck on a complicated problem, take one of the factors out and try to solve something simpler; then, go back to the more complicated case.

 

[TimeInquirer]

@PeroK your advice seems really helpful. Thanks a lot. I hope to update this thread later tonight after I finish my physics problems.