Being balanced means that your center of mass is supported by your body's structure. How is being rooted different from being balanced?
Being rooted means you can absorb/resist some force without moving. A dancer can be balanced on pointe, but this is not a good stance for rooting because they are easily unbalanced. Balance is necessary but not sufficient to be rooted. Fighting stances will have the feet separated and knees bent to help absorb force.
But this is not the end of the story. There are factors in addition to where your joints are in space and how they are aligned.
Here is an example that is easier to illustrate than explain mechanically:
- Stand facing a wall in horse stance
- Stand ~30 cm from the wall so you can easily push on the wall with a bent arm.
- [Make your lower body rigid]
- Now push lightly and continuously on the wall, without leaning. This push is perpendicular to the line drawn between your feet, and is the most advantageous angle to apply force to unbalance someone in a horse stance.
If you are rigid, you quickly rock back on your heels and start to fall backward. But if you relax your lower body, and in particular the area around your hips, you can absorb some push and feel this transmitted into the ground through your heels. There is no obvious change in appearance between these two states. Your center of mass is unmoved.
You can also do this drill with a partner supplying the push instead of pushing on a wall.