Hello dear Ecumene 
The following is also just my humble opinion about the topic:
I’m seriously developing my game for the time being, and i will need a physics engine for sure.
A few weeks ago i thought that i won’t be able to write a physics engine on my own. (Not just forces, AABB, Circles, but also with proper constraints etc…)
Then i started learning physic stuff, as i dislike using engines/libraries (apart from LWJGL, i’m glad somebody wrote the windowing system for me :))
After the initial bloodrush of maybe pulling of a half decent physics engine, i got to understand that there is MUCH more than just a little math and geometry. But i know that one day i will master it, and that will greatly help me with future 3d Projects. If i cant handle the 2D situation, i’m not ready for the third axis, for me IMHO 
If you want my advice, learn/try to understand the methods behind it, and get better at implementing your own, component by component, the knowledge won’t be lost! So basically what Gibbo3771 said.
Here’s a good starting tutorial, which explains a physics engine based on impulse resolution, but beware!
The code in the examples/code snippets (if it hasn’t been corrected as of lately), has quite a few errors.
So if you can read it for the sake of the ‘method behind it’, that’s great, if you need to copy the code to test it, not so great 
Here’s the link:
You also may like to read through the following tutorials about SAT (Separating Axis Theorem), which is also a good way of implementing a basic physics engine (without the whole architecture of something like Box2D), SAT does the collisions and you could add some basic force system to SAT, and that will also be quite challenging for the start i suppose 
Here the links:
- Nice explanation: http://gamedevelopment.tutsplus.com/tutorials/collision-detection-using-the-separating-axis-theorem--gamedev-169
- With flash examples to test the math: http://www.metanetsoftware.com/technique/tutorialA.html
Box2D documentation also helps greatly! Google for some good Box2D Documentation, it is well explained depending on what Docs you read.
Greetings and all the best
JJ