## The Mechanics of Airborne Rotation

Gymnastics is essentially the physical expression of biomechanical theories; in fact, there are a some skills in this sport (the Tkatchev on bars being the most well-known example) which were, so the story goes, dreamed up not by gymnasts, but by biomechanists. In this column, we’ll look at the basic principles of airborne rotation. First, some terminology:

Center of Mass: This is the average location of all the body’s mass. This is generally somewhere around the waist, but it varies to some extent depending on the body position.

Axis of Rotation: This is the imaginary line around which the body rotates. In the case of an airborne body, this line always goes through the center of mass. If we look at the body as a wheel, this would be the axle.

Angular Momentum: This is the amount of “rotating power” that the body has while airborne. You can think of this as the amount of torque applied to the wheel.

Once the body is airborne, its trajectory and angular momentum are irrevocably established. In other words, once a gymnast breaks contact with the apparatus, there is nothing she can do which will add height, distance, or angular momentum to the equation. (Technically, the gymnast is continually losing momentum to air resistance, but the effect is negligible in the context of gymnastics).

The gymnast cannot gain or lose angular momentum; she can, however, change how efficiently she uses that momentum. By redistributing her body mass closer to the axis of rotation, a gymnast can make more efficient use of her angular momentum, and thereby increase her rate of rotation.

To put all this information into context, we’ll analyze a very common skill: the back tuck on floor. On takeoff, the gymnast must push hard through the legs and toes (to establish upward momentum, which translates to height), while opening the chest and shoulders causing the arms to swing up and back over the head (to establish angular momentum). After the feet leave the floor, the gymnast must pull her knees towards her chest, curling into a tucked position (to bring her body’s mass closer to her axis of rotation, causing her rotation to accelerate). When the gymnast has completed a sufficient amount of rotation and made visual contact with the floor, she opens out of the tuck to a layout position (to redistribute her weight farther from her center of mass, causing her rotation to decelerate in preparation for landing). Finally, as her feet contact the floor, she must bend her knees to absorb as much momentum as possible, allowing her to stick the landing.

This is why a salto rotates more easily in a tucked position than in a layout position (as the weight is distributed closer to the transverse axis of rotation in a tuck than in a layout); it is also why a layout twists more easily than a tuck (as the weight is distributed closer to the longitudinal axis in a layout).

Each of these phases can be further broken down, and there are plenty of nuances which I haven’t covered here, but this should be enough to give a general idea of what’s going on when a gymnast is airborne.