Look up Box2D, it's a 2D physics engine, probably the best around.
I'm not sure about this because most of the time I use pure LWJGL, but I think that Slick2D comes with it and LibGDX also (which is great for android game development).
However, I'm sure that it wouldn't be too hard to implement it into a LWJGL engine. Edit:
And here you go: http://www.jbox2d.org/
If you aren't sure how to use it here's a cool video on it from "TheCodingUniverse".http://www.youtube.com/v/ZKJC2cloIqc?version=3&hl=en_US&start=