## Investigation 10 - Somersaults and Twisting

We look into more advanced tricks that involve somersaults and twists, and show how they are achieved.

### How can you achieve somersaults on the Trapeze?

In order to create Angular Momentum for rotation, an Impulse must be exerted on the body. This is achieved in complicated ways on the trapeze, but fundamentally comes from either pushing off or pulling on the bar. The resulting Impulse gives the flyer Angular Momentum, so that once they leave the bar, they start to rotate.

The relative Angular Velocities of the Double Layout and the Tucked Double Back Somersault demonstrate the principal applied to the ice skater in the previous section. The Layout is performed with a straight body, so I about the axis (through the hips) is very large. Angular Momentum is constant throughout, so a relatively slow Angular Velocity is achieved. This slow rate of rotation is very visible to spectators. In comparison, the Tucked Double Back Somersault is performed in a tucked position. I is therefore much less (body is more compact), and since the starting Angular Momentum is approximately the same as in the Layout, the Angular Velocity is much higher. The faster rate of spin is why Triple Somersaults are performed tucked (the flyer has to spin fast to get round three times in time to be caught).

More advanced tricks on the trapeze involve combinations of somersaults and twists before the catch. Although it is possible to twist before a catch, the movement before leaving the bar is different to that preceding a somersault, making it very difficult to combine the two. What the flyer needs to do is start to somersault, and twist while they are in the air.

This may appear to be a violation of the Conservation of Angular Momentum rule, since the flyer starts with no Angular Momentum about their twisting axis, and during the flight, they seem to create some without having anything to push off to provide a force. But there is no violation. Let's see why...

In order to understand how this is achieved, we must appreciate that a person is not a rigid object, and therefore there is only a certain distance that we can go, using a person modelled as a rod.

Let us assume that the flyer leaves the bar with a large, non-zero Angular Momentum. As they are initially just somersaulting (no twist to start with), this is a vector parallel to the axis of rotation through their hips. Since this Angular Momentum is conserved throughout the trick while they are in the air, the vector it corresponds to remains in the same direction, regardless of how much the flyer wiggles or changes their position. However, the axis about which the flyer rotates can change (the axis of rotation is always in the same direction as the Angular Velocity vector). In order to initiate twisting, the flyer 'throws' their arms round. This causes their axis of rotation to wander off the original direction of the Angular Momentum vector.

This then represents a threat to the Conservation of Angular Momentum principal, since the magnitude of Angular Momentum in any given direction has changed. This initiates a twist, creating exactly enough Angular Momentum about a twisting axis so that the vector sum of the two separate Angular Momentums is still the same as the original value. Angular Momentum has been conserved, and the flyer has initiated a twist in mid-air.

In layman’s terms: the flyer has created the twist by ‘stealing’ a bit of the rotation from the somersault so that the total amount of rotation stays the same.

It is interesting to note that this is only possible if the flyer starts with Angular Momentum in the first place.

Some figures can help to demonstrate the relationship between the angle between the axis of rotation and the Angular Momentum vector and the rate of twisting. In a Layout (back somersault with body straight), throwing the arms to create an angle of just 11o, causes the body to twist at a rate of 3 twists per somersault. In a Double Back Somersault, when the flyer's body is tucked or piked, throwing the arms will create an angle larger than 11o (since I is smaller). For an angle of 20o, the body will twist at a rate of five and a half twists per somersault.