Physics is physics, just use an existing java physics engine (Jbullet at this point) and run it on the server. Then since you already have the network layer, just make sure that you send the players the updated NPC positions.
Of course, I'm totally ignoring the effects of lag and ping here, because it really is a complicated mess and to do it right, you'll need to compute the physics on the client too. That way the client can predict where the server will have everything move, and then it will lerp its predicted positions to the server positions as needed. Then the server also has to validate anything the player says to make sure the player is following the physics rules.
So it will be very, very simple
It's all about an emu, we got a client and are making a gameserver. We are already on finishing steps, just missing geodata for the server.