### Re: What physic's are involved in trampolining

Date: Fri Aug 18 13:49:18 2000
Posted By: Tom Cull, Staff, Clinical Sciences MR Division, Marconi Medical Systems
Area of science: Physics
ID: 965530524.Ph
Message:

There are a few questions/responses posted on some aspects of trampolines already posted,

Much of athletics, especially gymnastics, ice skating, and diving involves control of angular or rotational speed. For example a "simple" front flip or somersault, can be executed very subtly so that it may appear that the spinning starts spontaneously. This is a very good illusion. Kenneth Law and Cynthia Harvey spoke of some of the illusions of dance in Physics, Dance, and the Pas de Deux.

Consider a dancer standing at rest. The center of gravity (or mass) is the position at which all the dancer's mass can be located to solve the static balance problem. A slightly different concept the center of force (a la Laws and Harvey) can be defined as the point at which a distributed force or collection of forces may be considered to act. The dancer needs to create a force inbalance to generate acceleration. Thinking about Newton's 3rd Law of Motion: For every force exerted by a body against something, the body experiences an equal and opposite force acting back on itself, the dancer needs to unbalance the equilibrium to generate acceleration.

A very subtle way to do this is lift a leg slightly forward to shift the center of force causing the dancer to start to fall forward. The center of gravity is ahead of the center of force creating an unbalance force and torque. Instead of falling flat on her face, the dancer places her foot down on the floor and then can begin running.

Divers or trampoliners do a similar thing by pulling a leg (knee bent) up and then placing it down quickly while flexing the other leg. When executed properly, this looks much more graceful than squatting down and pushing against the floor like a long jumper or a basketball player.

This same motion can be exaggerated slightly (still takes a lot of balance and talent, for sure) to generate a forward flip. At the point of pushing off the floor, the tumbler generates more torque by swinging her arms, tucking her chin in slightly and pulling her legs in. With the body compact in a somersaulting position the distribution of mass or momentum of inertia is relatively small compared to standing straight. The talented tumbler can flip 360 degrees (or more!) about a horizontal axis. The spinning can be stopped by extending the limbs which raises the moment of inertia. For the angular momentum to be conserved the angular speed (spinning) must slow down [Several postings on angular moment are available from the MadSci search engine].

Conservation of angular momentum is always true once the person leaves the floor. Any torque needed to create spin is created by the feet (or hands) on the floor and the speed of rotation is controlled by body positioning. Most twisting or flipping about any axis begins before the tumbler leaves the floor. The body generates the initial inbalance through friction between the floor (or trampoline) and the feet. Any other twisting must involve conservation of angular momentum so that if one part turns left, another equal amount of angular momentum most be generated turning right. This twisting the body in different directions while maintaining angular momentum conservation is how cats always land on their feet. Similarly, a trampoliner can can swing her legs left while turning her upper body and arms to the right.

Expert tumblers and divers spend a lot of time on presentation to create the illusion that the flipping and twisting occurs spontaneously in the air. In fact, in diving judges are often very critical on the take-off from the board. Hiding the momentum adjustments is usually easier for persons with a low mass to height ratio and/or extreme flexibility. Most divers are fairly tall for their weight which aids in moment of inertia control, while tumblers tend to be shorter which helps generate higher rotation most of the time. Divers have to typically twist very rapidly while falling and then stabilize before entry into the water. Gymnasts most work in powerful bursts and use the floor or trampoline and muscle force to stop rotation.

I reccomend you check out the gymnastics and diving during summer olympics. Without a doubt, you will hear a commentator say something that is physically untrue about the spinning of an athlete. Just remember that the athletes are just really good at maximizing angular momentum change with as little motion as possible.

Sincerely,

Tom "Spin Zero" Cull

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