I’m not at my own computer now but I’ll try to describe a simple case. Say you have a bone the head of which is free to move. Apart from the armature you have an object that responds to physics. On the bone you put a Track To constraint that uses the physics object as its target (what it Tracks To), and the Y axis enabled (this is always the axis along the length of a bone). Now the bone will point at the physics object when the physics object moves. If the physics object is set to respond to a force like gravity or wind, etc., then when it moves, the bone will follow & look also as if it’s being moved by the physics.
Another example would be pretty much the same but using a Copy Location constraint. Then the bone would need to be unconnected, able to move independently of other bones in the armature, which is how bones used as IK Constraint targets are often set up. Say it controls the IK chain for an arm. If the physics object is moved, the arm will respond to that motion, because it tracks the IK Constraint target bone, which in turn tracks the physics object.
These are only the barest sketches of such a setup, so if you haven’t used constraints before, look them and try a few examples to discover how they work. Very powerful animation tools.