# Physics of Gymnastics

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Gymnasts use physics everyday. As a gymnast I never realized how much physics went into every motion, every back handspring, every mistake on the bars. If gymnasts were physicists (or at least knew more about physics) they would be better equipped to handle the difficult aspects of gymnastics. As a gymnast I learned the motions that were necessary to complete the tricks that I was working on, and as a coach I taught others the same. I never truly understood why a particular angle gave me a better back handspring or why the angle that I hit a springboard at really mattered when completing a vault. We are going to explore some of the different apparatuses in gymnastics and a few of the physics laws that are involved in them. We will not even barely scratch the surface of the different ways that physics can explain gymnastics.

Newton's Laws

Newton's Laws can be found in the textbook, Physics for Scientists and Engineers by Serway.

Newton's First Law

An object remains at rest, or in motion, unless an external force acts upon it.

Newton's Second Law

The acceleration of a body or object is directly proportional to the net force acting on the body or object and is inversely
proportional to its mass.

F = ma

Newton's Third Law

For every action force, there is an equal and opposite reaction force.

The Floor

There are many aspects of physics found on the floor. The gymnast performs on a floor that "measures 12 x 12 meters, with an additional safety border of 1 metre. The performance area must have a surface elasticity, to allow for power during take-off and softness for landing." (FIG) The surface elasticity found in the floor mat gives the gymnast extra bounce which increases her momentum.

Let's examine a basic tumbling run. All three of Newton's Laws can be seen in this one tumbling run. We can see Newton's first law before the gymnast takes even one step. Until she takes a step, the gymnast is at rest. When she is ready to tumble the gymnast applies the force. A gymnast takes a running start when approaching a tumbling run, and as she is moving across the floor she is increasing her momentum. This is a demonstration of Newton's second law.

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### Popular Essays

The landing is also a demonstration of Newton's second law. At the end of the rotation of the salto that the gymnast above is performing, she opens up and spots the ground. This stops her rotational momentum, the same way that a figure skater slows down her rotation, which increases the time that it takes for the gymnast to land. Because force is equal to the change in momentum divided by the time, this decreases the force that the gymnast exerts on the ground and allows for an easier landing.

The Bars

The bars are another apparatus that shows many different aspects of physics. Let's explore two of them.

The Law of Conservation of Angular Momentum

"The total angular momentum of a system is constant in both magnitude and direction if the resultant external torque acting on the system is zero." (Serway 345)

This means that when a gymnast is spinning around the bar, unless there is an external force acting on her, she will continue to spin. Gymnasts use this basic principle to perform giants on the bar. They also increase their momentum using their body positions to decrease the moment of inertia.

Forces of Kinetic Friction

When you see a gymnast gearing up for her bar routine you may notice all of that white chalk that is floating around in the air. Little known to most gymnasts, they are using that chalk in order to put to work the forces of kinetic friction. The chalk that is on her hands helps to increase the coefficient of friction between her hands and the bars, without it her hands would become extremely slippery and she would move to quickly on the bars and eventually slip right off. This is also the reason that gymnasts sport those attractive grips on thier hands. With a dowel rod that is held parallel to the bar and an abrasive surface, it too increases the coefficient of friction and therefore gives the gymnast a better "grip" on the bar.

The Rings

When a male gymnast performs the iron cross on the rings he appears to be achieving 90° angles between his body and his arms. We can use Newton's laws to determine if this is actually possible.

Calculations:

F = ma
x: Tsin 0° + Tsin 0° - Mg = 0

We will assume that the mass of the gymnast is 70.0 kg and because we can not have a denominator of 0 we will choose an angle that is close to zero so the equation is as follows:

Tsin 1° + Tsin 1° = 70.0 x 9.81 m/s2
T = 70.0 x 9.81 m/s2
sin 1° + sin 1°
T = 19673.51 N !!!!

This is an extremely large force and no gymnast, no matter how strong he is, would be able to hold an iron cross with that much stress (tension) on his arms.

Bibliography

FÉDÉRATION INTERNATIONALE DE GYMNASTIQUE. "Technical Regulations 2005." 2004. 24 October, 2004.

Serway,Raymond A., et al. Physics for Scientists and Engineers - 6th ed. Belmont: Thomson, Brooks/Cole, 2004.

"Gymnastics Clip Art Galore." http://www.gymclip.com

"Drills and Skills Page." http://www.drillsandskills.com

"The Physics of Sports." http://home.nc.rr.com/enloephysics/sports.htm

Fink, Hardy. Technique. "An Insight into the Biomechanics of Twisting." February 1997, Vol. 17, No. 2.

"The Gymnast Corner" http://www.geocities.com/bright_effect/ironcross.html