1. Why the Amount of Rotation in a Somersault Is Decided at Takeoff, Not in the Air
The amount of rotation for a somersault cannot be increased while in the air. According to materials summarizing the mechanics of diving, the amount of rotation (angular momentum) that serves as the basis for a somersault must be created during the takeoff [1]. While gravity acts in the air, there is almost no external force turning the body around its center of mass, so changing posture does not change this total. In gymnastics, it is also explained that the amount held at the moment of leaving the ground remains constant in the air [2]. Diving materials list three ways to start rotation: leaning the body forward, transferring recoil into rotation, and pushing with the feet in a direction offset from the body's center [1]. However, which of these is used in specific gymnastics moves cannot be determined from this information alone. If the amount is decided at takeoff, is there nothing left for the athlete to do in the air? Actually, even if the amount of rotation is the same, the speed of rotation can be changed.
2. Why Curling Up Speeds Up Rotation: The Radius of Rotation Gets Smaller
In figure skating spins, when a skater pulls their outstretched arms close to their body, the rotation speeds up. One explanation states that "mass × radius × speed = angular momentum is constant" [3]. If you pull the arms in to make the radius smaller, the speed increases to keep the angular momentum the same. However, this formula is a simple explanation assuming a point-like object; for the human body, moment of inertia is used. Curling up for a somersault uses the same concept. For an object that changes shape like a human body, it cannot be represented by a single radius, so we consider "moment of inertia," a quantity representing resistance to rotation. The speed of rotation is determined by dividing angular momentum by moment of inertia. The more you curl up and gather your body around the center, the smaller the moment of inertia becomes, and you spin faster with the same angular momentum [2]. Diving materials state that in a comparison between a fully stretched position and the tightest tuck, the tucked position can rotate about 4 times faster [1]. It is not always 4 times. Looking at the calculation in reverse, it means that when the moment of inertia becomes one-fourth, the speed becomes 4 times.
3. Why Athletes Stretch Their Bodies Before Landing: To Slow the Rotation
If curling up makes you spin faster, why not stay curled up? If you did, you would rotate too much before landing. To prepare for landing, athletes stretch their bodies, slow down the rotation, and point their feet downward. Choosing the rotation speed yourself is the key to a somersault. A somersault with the body stretched out (layout) is said to require more rotational momentum than a tuck [8]. Because the moment of inertia is larger, the rotation is slower with the same angular momentum, so a larger angular momentum is needed to complete one rotation.
4. Where the Twist in a Twisting Somersault Comes From in Mid-Air
In moves that add a twist to a somersault, the twist is also a form of rotation, so it must be created somewhere. When angular momentum for twisting is created during takeoff, it is called a "contact twist." A 3D analysis study from Nippon Sport Science University on a back layout double twist found that contact twist was created at takeoff for this move, and the whole-body twist was adjusted by arm movements in the air [4]. The method of use differed among athletes [4]. Why can moving arms in the air adjust the twist? According to mathematical analysis, changing the shape in the air causes the body's axis to tilt relative to the direction of rotation, and a twist can occur even if the total angular momentum does not change [5]. It is thought that Frohlich's 1979 paper was the first to correctly explain the physics of twisting somersaults [5]. When a cat changes direction in mid-air, the angular momentum remains zero. A twisting somersault athlete has angular momentum, so it is a different case.
5. The Moonsault: A Double Backward Somersault With One Twist
The moonsault is a move involving a backward double somersault with one twist. Mitsuo Tsukahara performed it as a dismount from the horizontal bar in the team free exercise at the 1972 Munich Olympics [6]. It is said that Tsukahara got the idea from the trampoline move "half-in half-out" [6]. In cases where an athlete enters the air with angular momentum like this move, it is explained that it is important to match the timing of the rotation and the parabolic motion of the center of mass to land on the feet [7]. It can be described as a move that masters the amount decided at takeoff by curling, stretching, and twisting.
6. How to Try It Yourself: Folding Your Arms on a Swivel Chair Changes Rotation Speed
The mechanism of spinning faster when curling up can be checked at home. If you have a swivel chair, sit down, spread your arms, lift your feet slightly off the floor, and have someone spin you slowly. Then, pull your arms to your chest and see how the rotation speed changes. If you do not have a chair, try standing in an open space and slowly spinning while folding your arms. Because there is friction between the soles of your feet and the floor, it may not speed up cleanly. First, check that there are no objects around you, and do it slowly. If you feel dizzy, stop immediately and sit down. Try this with an adult. Next, if you have a chance to watch videos of somersaults, look at where the athletes curl up and where they stretch out to use the rotation decided at takeoff.