Humans can do things. Awesome things. Case in point: this human, named Aaron Cook. Cook can do some serious tumbling (just check out his YouTube channel), but he can also do something extremely difficult—a standing double back tuck (backflip).
I have two daughters and both are gymnasts, so I know just how difficult this move really is. A back tuck is a flip in which the feet move forward and the head moves back (a front tuck is the exact opposite). The "tuck" part means that Cook pulls his legs into his body as he rotates. If he stayed in a straight position, it would be called a layout—and it would be super impossible. Last, we have the "standing" part. This means that he does the flip from a standing position. It's actually much easier to do a double back tuck if it's part of another tumbling pass where the gymnast builds both energy and rotation over the course of several moves.
Why is the standing double back so difficult? Well, you have to do two really hard things to not crash on your head.
First, you have to jump high enough so that you are in the air long enough to rotate. Notice how my daughter's center of mass rises and then moves back down.
Second, you need to rotate—twice. There are two things to helps with this rotation. In order to start the rotation, Cook swings his arms. This motion gives him an initial angular momentum. Angular momentum is very similar to normal momentum, but instead of being the product of mass and velocity, angular momentum is the product of "rotational mass" and angular velocity. The rotational mass (usually called the moment of inertia) depends on both the mass of the object (or human) and how this mass is distributed. Once he is in the air, he pulls his legs in close to his body. This decreases his rotational mass so that his angular velocity increases.
Here is another way to do a back tuck that is a little bit easier (according to my daughter). In this version, she starts in a handstand. As she moves back to a standing position, she increases her angular momentum so that she will rotate faster once she does the flipping part.
The fact that Aaron Cook can make this standing double back tuck kind of makes him a superhero. Looking at the video, I can measure the time he is in the air with a hang time of approximately 0.867 seconds. Since the vertical acceleration is known (-9.8 m/s2), I can use the normal kinematic equations to make a relationship between time and maximum height. If you want all the details of this calculation, you can find them in this older post.
With this hang time, Aaron Cook jumps a height of 0.92 meters. That might not seem very high, but remember that is the change in position of his center of mass and not his feet. During that time he rotates twice. So, I can calculate his average angular velocity with a rotation of 4π radians. This gives a rotation rate of 14.5 radians per second or 138 rpm. Yes, that's fast. I don't recommend you try this on your own.
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