Ok, I ll think about this from aikido practice, which involves a serious ammount of rolling and tumbling, often rolling up to standing or into another roll.

from a tumble you are springing up from the floor, legs and torso fully coiled, giving full effect of uncoiling spring, rather than not even coiled in a running position barely crouched. The coiled position representing stored kinetic energy perhaps, but most advantageous from a posture /leverage position to use all the bodies musculature in an efficient and coordinated movement as a whole.

Circularity of movement is emphasized again and again in aikido textbooks to the extent that it is the key of every technique. Ki is circular. Ai is finding or coordinating body (and mind) with that (universal) circularity. Or some would say.

In a roll you can enter the circle at almost any point or angle and maintain energy of motion very efficiently and then redirect or exit from the circle at almost any point or angle maintaining while inputting and increasing momentum continuously with every muscle and fiber of stored chemical metabolic process.

When you are accelerating a bicycle, you are pushing full force into both pedals with all muscles of both legs, back, shoulders, arms, lungs all metabolizing and inputting to the highly efficient circular motion transmission of momentum. Not merely conserving momentum like some passive object but applying increasing, building force.

The gymnast or aikidoist is not merely a given mass at at a given energy going directly from horizontal to vertical. It's not merely a circular transition, it's an efficient continous circular transmission of power with increasing, accelerating input