PD game Mouse impossible comes to mind. I don't remember much in the way of other objects than your cannonballs moving but it was a nice physics puzzler.
Also old boardgame crossbows and catapults, Ah, that was great.
I've also only watched a video of angry birds but I think you could get quite far with something like this on amiga. Scale back the number and detail of simulated objects to suit the target processor power. And for drawing the graphics, why not try B&W wireframe in 1 bitplane. If you could get the animation to look smooth and realistic like angry birds, even in B&W it would be a pretty unique thing on amiga.