Ogre is just a 3D rendering library, so your choice of a physics library is - well, your choice.

So, what's the best physics library?
Kojack summed it up nicely:
Kojack wrote:Yeah, it's hard to point to any one engine as definitely the best, since they are all quite different. They have different collision shapes (Havok has cylinders, PhysX doesn't), different joints (I think Newton had a corkscrew joint which Havok might have too, but nothing else does) and various other issues.
Then there's the api, Newton is based entirely on callbacks (which I don't like), Havok is painfully SSE obsessed (get used to vector math which looks like C rather than C++. Good for performance, but is annoying to use), PhysX needs that stupid driver crap otherwise it's dll won't start, etc.
The most feature filled one is Havok. The animation system alone is enough reason for it (full skeleton animation with physics interaction, skeleton retargetting, inverse kinematics, export tools, etc). Plus if you pay massive amounts of cash you can get Havok Destruction, Havok AI, Havok Behaviour and other bits. (The basic Havok physics and animation components are free for pc).