When athletes hurl themselves into the air to perform a flip, the only force acting on them is gravity. Since gravity only affects their "center of mass," it cannot apply forces in a way that changes the athlete's spin. But the gymnasts can do that for themselves by using the conservation of angular momentum.
By changing how their mass is arranged, gymnasts can change how fast they spin. You can see this in the dismount phase of the uneven bar competitions. When a gymnast comes off the bars and performs a flip by tucking their legs inward, they can quickly increase their rotation rate in midair.
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