[![Rocking chair][1]][1]

I've replaced the rocking chair with a circle with a smaller inset circle representing the centre of gravity (CoG). The weight is $mg$.

Now assume there's plenty of friction between the circle (rocking chair) and floor, so as to prohibit any sliding/slipping.

At this point the distance between the vector $\mathbf{mg}$ and the vertical running through $\text{O}$ is $L$.

Gravity now forces the CoG to be lowered. A torque $\tau$ *about* the point $\text{O}$ arises:

$$\tau=mgL$$

This torque causes rotational acceleration of the circle:

$$\tau=I\alpha$$

This angular acceleration causes not only to move the CoG downward but also to the right.


  [1]: https://i.sstatic.net/QoBwO.png