Momentum and Moment of Inertia: Understanding “The Biles”

When I was a kid, my father was a high school gymnastics coach. His love for the sport led to me being enrolled in a park district camp to introduce me to it and it was then that I learned I was deeply afraid of heights. Maybe my immediate distaste for being off the ground ruined my gymnastics potential (sorry Dad!), but it only added to my appreciation for those who are good at it! With the Tokyo Olympics just around the corner, let’s talk about the absolute GOAT – Simone Biles.

Simone Biles, born March 14, 1997, stands 4’8”. The Columbus, Ohio, native became a household name in the last half decade as the most decorated US gymnast of all time, toting 30 Olympic and World Championship medals. In numbers alone, Simone stands tall as a legendary athlete, but she also makes her mark in gymnastics by doing impossibly difficult skills. Most famously seen at the 2013 World Championships, I’m talking about “The Biles.” In the video below, the skill can be viewed at 0:28.

“The Biles” is a move done during a floor routine. It is done on a tumbling pass and requires the gymnast to do two flips in layout position (no tucking or bending of the knees) with a 180-degree twist at the end of the second flip. Because of the 180 degree twist, the landing becomes even trickier. Simone created the skill and very few other gymnasts in the world can successfully perform it because of the mechanics behind the move! In order to understand why this is true we must investigate two main concepts: moment of inertia and conservation of momentum.

Moment of inertia is basically the rotational equivalent of mass. By that I mean, just as mass decides how much force it takes to accelerate an object a certain amount, moment of inertia decides how much torque it takes to reach a specific angular acceleration. The moment of inertia is all dependent on how far mass is from an object’s axis of rotation. The farther the mass is, the higher the moment of inertia and the higher the moment of inertia, the more torque it takes to accelerate. The video below shows a common physics lesson used to demonstrate this concept.

Momentum is a vector made up of mass multiplied by velocity and the basic idea is that in a closed system the total change in this value is always zero. There are two basic types of momentum—linear and rotational—with rotational momentum being an object’s moment of inertia multiplied by its angular velocity. In a system with no external forces being applied, the sum of the linear and rotational momentum is at a constant value until a force is applied to change that.

Combining these concepts, you can understand the difficulty from a physics perspective of “the Biles.” Remember that the move is two flips in a layout position, and with our new mechanics perspective that means two things: because of moment of inertia, we know the layout position is far more difficult to reach the required angular acceleration than in a tucked position and because of conservation of momentum we know everything that Simone does once she leaves the ground is due to the initial momentum that she takes off with. So not only does she need to create enough momentum to sustain the translational movement from her starting position, through the air, to where she lands, but she also needs to create enough momentum for the flipping and the twisting simultaneously.

If I didn’t appreciate her talent enough as a wannabe athlete, I sure do appreciate it as a mechanical engineer! How is it possible for Simone to do this? To start, her extreme strength and perfect timing allows her to create a crazy amount of momentum from her run-up to the tumbling pass. Another really important factor though is her height. Moment of inertia depends on the distance of the mass from the axis of rotation, and Simone is short. So, because her mass is not as far away from her axis of rotation as it is for other gymnasts, she has a physical advantage when it comes to completing this skill.

Apart from the necessary strength and low moment of inertia needed, Simone also must have incredible spatial awareness. In all gymnastics skills, it depends heavily on timing, on slight changes in one’s moment of inertia to create angular acceleration, and on controlling the redirection of momentum. Simone uses the position of her arms to induce her twists and rotations through the air.

If this wasn’t cool enough, Simone competed in the World Championships in November of 2018 where she won four gold medals, with one being in all-around, and she unveiled “the Biles” on vault. The most impressive part is that she did all this with a kidney stone!

Maybe my fears keep me from doing most of the basic skills in gymnastics, but my love for mechanics lets me appreciate the sport as well as the athletes in a special way. Gymnastics is a great sport to look for examples of conservation of momentum and the importance of moment of inertia, but don’t limit yourself - you can find examples in every sport! Next time you’re watching curling or whatever is on ESPN2 on a Sunday afternoon keep your eyes peeled for these examples of mechanics.

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