Technique with Taucer: The Physics of Gymnastics, Part 1

I’d love to see one or more columns on the physics of various gymnastics skills, especially on bars. I took up a different flying-through-the-air sport as a young adult and was always fascinated by the conversion of linear motion into rotational motion.

-mommyof1

Before I start, let me just thank mommyof1 for handing me this blank check to nerd out about one of my favorite topics. This will be a multi-part series, and I probably won’t get to bars until part two or three at the least. I will also include some simple physics experiments you can safely do at home to demonstrate some of the principles we use in gymnastics, and if you are the parent or guardian of an athlete, I highly recommend inviting your athlete to join you for these experiments.

Anyway, let’s get to it.

The short answer

There’s no short answer. 

In this month’s column, we’ll look at a few physics concepts that form the necessary basis needed to understand the principles at work in gymnastics. These concepts are center of mass, linear momentum, and angular momentum. We’ll also look at some simple experiments you can do at home to demonstrate these concepts.

The long answer

The first physics concept that we must understand is center of mass (CoM for short). Everything else we’ll be discussing in this series revolves around the CoM, both literally and metaphorically.

The CoM is the average location of the gymnast’s mass. While the athlete is airborne, the CoM will follow a parabolic path which is irrevocably determined when the gymnast becomes airborne. The center of mass also acts as the central point around which all rotation occurs.

To illustrate this concept, there is an easy set of experiments you can perform (preferably outside). For this experiment, you will need a stick or rod (ideally somewhere near two to three feet long), a plunger, and some tape.

Put a small piece of tape around one end of the rod, and another piece of tape around the center of the rod. Hold the rod out in front of you, throw it up in the air, and spin it as you throw it. First, watch the tape on the end. You’ll notice it follows a complex path, circling but also rising and falling as the rod goes up, reaches its peak, and then begins to fall. It would be very difficult to predict ahead of time exactly what path the end of the rod will take as it flies through the air.

Now throw it again the same way, but this time watch the center of the rod. As the rod rises and falls, regardless of its rotation, that center point will follow a very simple, easily-predictable path. If you throw the rod straight up, that center point will go straight up and down; if you throw it with some horizontal movement, it will follow a parabolic path that curves towards the ground.

That center point is the CoM.

Now, grab the plunger, and once again spit it up in the air. Because there is a dramatic imbalance in the weight distribution, the center of mass will not be at the midpoint of the handle; rather, it will be very close to the head of the plunger. The handle will rotate around the head, because that is where the CoM is. Once again, the CoM will act as the center of rotation, and will trace a very simple and predictable path through the air.

For gymnastics purposes, the CoM is approximately in the athlete’s waist. Its exact location varies depending on body position—in some circumstances it can even be outside the athlete’s body—but if we generally assume the waist to be the center of mass, that will be close enough for our purposes.

From here, we’ll move on to discussing force and momentum, which comes in two forms: linear and angular.

Linear momentum is what happens when force is applied through an object’s CoM. In a zero-gravity environment, any linear momentum that an object has would cause its CoM to move indefinitely in a straight line. In an environment with gravity, this path will curve downward.* Once the athlete is airborne, the parabolic path of their CoM is set in stone; there is nothing they can possibly do to change how high or how far they’ll go before landing, unless they come in contact with some external object (a bar, a vault table, a spotter, etc).**

Angular momentum is what happens when we apply force to an object that does not go through it’s CoM, but instead is applied at an angle. Angular momentum causes the object to rotate around its own CoM. Unlike linear momentum, angular momentum can be manipulated while airborne.***

To illustrate these two concepts, we can perform a simple experiment using a swivelling wheeled office chair. Make sure you have a bit of room around the chair (and a hardwood floor will make this work better).

Stand or sit in front of the chair, put your hand on the front of the seat, right between where your knees would be if you were sitting, and push directly forward towards the center of the seat. The chair will roll backwards and, assuming all of the wheels are rolling cleanly, it will travel in a straight line with little or no rotation. By pushing through the chair’s CoM, you have created linear momentum, causing the chair to move backwards in a straight line.

Now, put your hand in the same spot, but this time instead of pushing directly forward towards the center of the seat, push to one side. The chair will not travel much, but will spin in place. By pushing in a direction which is tangential to the CoM, you have created angular momentum, causing the chair to spin.

All gymnastics skills revolve around generating and manipulating linear and angular momentum. If the athlete wishes to rise, she must generate upward linear momentum. If she wishes to travel in any direction, she must generate linear momentum in that direction. If she wishes to rotate, she must generate angular momentum. The sport of gymnastics, at its core, is little more than the precisely-controlled generation and manipulation of these two types of momentum.

The author’s opinion

The laws of physics are not just useful; they’re beautiful beyond description. Each and every gymnastics skill is a delicate dance. Like any dance, it requires trust, respect, and confidence

It is not necessary or practical for all athletes and spectators to take a full physics course to understand and perform gymnastics skills. However, I firmly believe that both athletes and spectators benefit from having at least a general understanding of the mechanics of the skills. An understanding of these underlying mechanics unlocks a deeper understanding and appreciation of the skills being performed.

*Technically, the CoM is following a straight path through curved spacetime, but general relativity is well beyond anything we need to know in order to understand gymnastics, so (much to my disappointment) we won’t delve into it here.
**We’re ignoring the effects of air resistance because their effects are negligible in the context of gymnastics. We’re also assuming the athlete is not wearing a jetpack.

***The net amount of angular momentum and its direction cannot be changed while airborne, but the athlete can make adjustments to how efficiently they use that momentum, thus changing the speed at which she rotates. We’ll delve into this more in part two.

Geoffrey Taucer