The amazing physics of Simone Biles’ double pike

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It’s gymnastics an extremely difficult sport, and not just extreme for Olympic athletes like the five-time (so far) Simone Biles medal. Physics is also quite challenging. Consider something seemingly simple, like a flip.

There will be some version of the reversal of all four women’s gymnastic events: floor, bars, vault and beam. It is one of two types of rotations that a gymnast can make in the air. In a physical sense, turning is a rotation of the head to the feet around an imaginary axis that passes through the gymnast’s hips. For another type of rotation, a turn, imagine an axis going from their head to their feet.

Maybe it’s easier to just see them. These two animations were created in Python. (You can see the code here i here.)

A trifle over Rhett Allain
A trifle over Rhett Allain

A gymnast can perform both of these types of rotations at the same time – that’s what makes the sport so interesting to watch. In physics, we would call this type of motion “rigid rotation of the body.” But it is clear that humans are not rigid, so the math to describe such rotations can be quite complicated. For the sake of brevity, let us limit our discussion to a reversal.

There are three types of rollovers. There is a schedule in which the gymnast keeps his body in a straight position. There is a pike in which the hips bend at an angle of about 90 degrees. Finally, there is the bent knees, raised towards the chest.

What is the difference in terms of physics?

Rotations and moment of inertia

If you want to understand the physics of rotation, you have to consider the moment of inertia. I know it’s a sound expression. Let’s start with an example that involves boats. (Yes, boats.)

Suppose you are standing on the dock next to a small boat that is just floating there and not tied up. If you put your foot on a boat and push it, what happens? Yes, the boat is moving away – but it’s doing something else. The boat too accelerates as it moves away. This change in speed is acceleration.

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