Final answer:
The hand-operated rotary device also known as a type of swimming kick is called an eggbeater. It is used in maneuvering the legs in water sports such as water polo and synchronized swimming for stability.
Step-by-step explanation:
The name of the hand-operated rotary device that is also a kick used in treading water is called an eggbeater. This term is not only associated with a kitchen tool but also with a swimming technique that is particularly effective for maintaining a position in the water without sinking, a skill which is especially useful in water polo and synchronized swimming. When someone uses the eggbeater kick, they move their legs in a circular motion similar to the way an eggbeater is rotated, which provides upward thrust and stability in the water.