Let us assume that the centre of gravity is moving forward. This could be because we are swaying forward, bending forward, or lifting something heavy. The shift in the centre of gravity is detected, usually through proprioception.
Moving forward involves forward momentum. A good illustration is coming off a moving belt at an airport. There is a moment of imbalance which we can perceive and during which most of us struggle for balance.
Turning fast, such as in dancing and in figure scating, make it difficult to stop turning. Most of us have to struggle for balance after turning fast.