The speed of your turns is the most challenging part, but not the most important part.
One of the most common issues I see in turning is the desire to mask poor preparation positions with more powerful and quicker rotations. The quality of the preparation is what sets the turn on course to be stable and centered on the supporting foot or travel around the gym floor. Preparation refers to the position of the free leg, your arms, your supporting foot, and the direction of the body. If these body parts and lines start from the correct positions and maintain correct alignment, then the pivot has a strong likelihood of rotating in the correct way.
To check your own preparation positions, perform each starting position without actually rotating. Focus on shifting all your weight onto the supporting leg. Set the free leg and arms into correct positions. Balance on that foot and take a controlled relevé up into the turning position and hold for a few counts before lowering down. Be mindful not to use your arms and shoulders to help find this balance; these should be set in their proper place at the onset of the relevé.
If you have a stable preparation balance, test the position with just a quarter or half turn to see if this stability is maintained through movement.
It is common for balance to fall to the heel of the foot, the inner side, or the outer side during a relevé. Any of these slight adjustments of weight in the preparation can result in a pivot that is traveling instead of centered in the foot. The relevé should be measured to allow your ankle, knee, and hip to find their proper alignment. The free leg should be able to take its place without changing the position of the pelvis.
The reason for starting with slow turns and working your way up to more power in the turn is to make sure the body’s architecture holds up from start to finish, which can be more difficult to determine when rotating quickly.
For example, when you finish a pivot several steps away from where you started, this could mean the weight drifted in your balance in preparation to the turn and then traveled as you turned.
Once you have a solid, stable preparation position to start your pivots, begin to explore the arm swings. Aggressive arm swings can cause the shoulder line to rotate into position before the hips and cause a loss in turning stability. If you use music for your turns, make sure the timing and placement of the arms is consistent. Slower turns can be helpful to make this difference more apparent.
Be mindful that finishing a skill is a key part of the skill itself. The relevé should be coming up to the finishing position with a lifted body and controlled supporting leg. Take steps that are intentionally placed and not just the result of gravity pulling you down to the floor. The end of the pivot should lead directly into a wave, a balance, a series of steps, or handling with the apparatus.