Let's Do Some Flippin' Physics

The most exciting part of gymnastics is always the high flying flipping elements they perform. For my physics capstone I decided to analyze a tuck kick out on a trampoline. I wanted to find out the best way to do a tuck kick out, one that is the most aesthetically pleasing to watch.

Moment of Inertia

In gymnastics there are 3 basic positions when flipping: tuck, pike, and layout. When performing skills, gymnasts change their body shape and in doing so change their moment of inertia. They often use this to their advantage, tucking or piking to increase their rotation and laying themselves out to slow down their rotation. Moment of inertia for the human body is difficult to calculate since a human is a very irregular shape. However, we can simplify this by using regular shapes like a sphere and a long rod.

To see how much someone slows down in the laid out position you must look at the following equation:

L= I w

L remains constant unless there is a net torque acting on the system. In this case, there is no net torque on the system. Therefore, you can state that L sphere= L rod

Using the given measurements of my body

Radius of Tuck= .23275 m
Length of Lay out = 1.68402 m

L sphere = L rod
3/5 m r^2 (w) = 1/12 m L^2 (w)
3/5 (.23275 m) ^2 (w)= 1/12 (1.68402 m) ^2 (w)
.236/.0325 = 7.26

The angular velocity of my tuck is about 7.26 times faster

In the video above you can see how the vaulter uses moment of inertia to his advantage. He elongates his body at the beginning of take off. This is the laid out position. Then he folds himself into a pike position to create enough acceleration to make 3 rotations. Before landing, he slightly opens up his body again to decelerate his angular velocity once again to stick the landing.  

Video Analysis (The Kinematics)

4 Mediocre Attempts at a tuck kick out #Rio2016

I used Logger Pro to do video analysis of the x and y positions and x and y velocities of my center of gravity. It showed that my body positions do not affect my speeds in the x and y direction as well as my position on the x and y axis. The x and y position graph was a symmetrical parabolic curve just like any other projectile. This means my velocity did not change even with the change in body shape. I follow the same basic principles of physics. I accelerate towards earth at around 9.8 m/s/s no matter what position I am in.

These are the results of my video analysis:

Max Height = 3.867 m

Average Y Velocity= 4.223 m/s

Average Y Acceleration= -9.331

Still, you can see in the video that I do not always go the same height in each flip. In fact, one flip traveled further along the x axis than the others and had significantly less height. If you look closely, I do not set my arms up. I throw them back. What determines the positions and velocities of your flip is not body position. It is the amount of energy you put into it and the angle of your take off.   

As you can see, this gymnast still falls at around 9.8 m/s/s towards the earth. He attempts to use a change in moment of inertia to his advantage by compressing his body into a tucked position, but his angle of take off and energy put in was not enough to give him the proper height. #NotRio2016

Video Analysis (Rotational Motion Style)

I video analysed the x and y positions of my feet this time. Then using a calculated column, I found the angle between the positions of my feet and my center of mass at different times. This angle, θ, I graphed vs time.

Here you can clearly see there is a difference in the tuck and laid out positions. The smaller angle measures represent laid out position and the larger angle measures represent the tucked position. I separated these two sections of the graph and found the slope of each. The slope of the graph is average angular velocity of my flips.

Average Angular Velocity of a Tuck = 2.25 rev/sec

Average Angular Velocity of a Lay Out = .10 rev/sec

Then I created another calculated column of the derivation of θ in order to graph angular velocity vs time.

Here you can also see the two separate portions of the graph that represent the different positions. The slopes of this graph are the average angular accelerations of the tuck and lay out positions.

Average Angular Acceleration of Tuck: 20 rev/sec

Average Angular Acceleration of Lay out: 1.20 rev/sec

To see all data and calculations visit this google doc link :


So What's The Best Way To Do A Tuck Kick Out?!?!?!

The best tuck kick out maximizes the amount time in the laid out position and minimizes the amount of time in the tuck position.

Given the parameters of my own tuck kick out this includes:

-Same amount of energy put in
-Same Angle of take off
-Same height achieved
-Same amount of flight time

Maximum Time in Layout=1.43 seconds

Minimal Time in Tuck=.07 seconds


Body shape does not alter the kinematics of your flips.

Change in moment of inertia can speed up or slow down your rotation.

Tuck less ... Lay more

Physics is flippin' awesome.

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