Physics of a Cartwheel

I did gymnastics for 12 years, and while I can’t do all of the flips and tricks that I used to be able to do, I still have a cartwheel or two up my sleeve. The cartwheel is a basic and essential component of gymnastics as well as many types of dance. It is an acrobatic movement in which the body does a complete circle using the “hand-hand-foot-foot” method. It also happens to involve many of the physics topics we have discussed this semester.

I have attached a video of me doing a cartwheel:

The front foot acts as the fulcrum about which the circular motion begins. In general, it is easier to complete the cartwheel when the fulcrum is farther away from the back leg. Also this makes the center of gravity be closer to the ground, which provides more stability. In the cartwheel there is both rotational and translational motion. When the hands are pushing down on the ground, there is an equal and opposite force of the ground pushing back up on the hands.

Newton’s second law is F=ma, so the larger the mass of the person doing the cartwheel the more force they will have to exert.

Impulse is force times change in time, and the larger the applied impulse, the larger the magnitude of velocity of the cartwheel.

I then compared a regular cartwheel with legs outstretched to one where my legs were bent:

I used a stopwatch to time the two cartwheels. When I do the cartwheel normally with my legs fully extended, it takes 1.06 seconds from when my first hand hits the ground to when my first foot hits. However, when I curl my legs in, it only takes .74 seconds. This relationship between radius and velocity can be shown with the equation KE = ½I⍵f2. I (moment of inertia) is dependent on radius, so when the radius is bigger the moment of inertia is bigger. Because of conservation of momentum, that means ⍵ must increase. Thus, when the radius is made shorter by me pulling in my legs, the cartwheel is faster.

Finally, I did a roundoff. A roundoff is the next level up from a cartwheel and is when your arms and shoulders act as more of a spring, which gives the end of the roundoff more power. Most notably it also ends in two feet together, rather than one after the other:

In my roundoff I observed how my arms and shoulders acted as a spring. Mostly it is the shoulders that “block” and result in the push off, which is a motion kind of like shrugging. For simplicity sake though we will look at my arms. If we say that the spring coefficient is 100N/m and my arms bend .05m, the spring force would be 5N of force in the opposite direction of displacement.

Note: if chosen to present in front of the class, I would be happy to show either the videos or do a live demonstration of my cartwheel skills.