Gymnastics and Physics

[gymluvr33]

I am doing my science fair project on why ro bhs back layouts take longer and rotate more slowly than ro bhs back tucks. I know that someone (I believe that it was TumblerK, but I'm not sure) wrote a thread about the physics in gymnastics. I am not just looking for answers for a project, but I was wondering if anyone would be able and willing to share some of the science behind my topic. Thank you so much.

-gymluvr33

 

[Geoffrey Taucer]

What you're looking at is conservation of angular momentum. I have not taken any formal physics courses, but my old coach was a physics nerd and taught us a lot of this stuff as part of our training. There are other coaches who can probably describe this better than I can, but I'll take a shot at it.

First, let's define a few terms:

Center of mass: The point around which your body rotates when you flip; for the purposes of this discussion, we can generally consider this to be somewhere around the waist.

Radius: The distance from the center of mass to the furthest point on your body (ie the radius of the circle drawn by your flip)

Angular Momentum: The amount of power you have behind your rotation.

Angular velocity: The speed at which you rotate.

Once your feet leave the floor, your angular momentum remains constant until you land (technically, air resistance will slightly decrease angular momentum through the course of the flip, but the effect is negligible).

By bringing the legs closer to the center of mass (ie tucking), you decrease your radius. Simple geometry shows that this decreases the distance the outermost parts of the body have to travel in the course of the flip -- and since the angular momentum is constant, this means that your rotational velocity increases.

In other words, there's an inverse correlation between radius and angular velocity.

There are a few aspects to this on which I'm not completely clear, such as how the distribution of mass can effect this.

I'm sure there are other coaches here who can explain this in more detail than I can. Anybody else want to weigh in? Did I miss anything?

 

[gracefulone]

The one thing you didn't mention, GT, was inertia, which is the summation of why a different body shape changes rotation. Inertia is why you turn faster when you pull your arms in, why that turn with leg above horizontal is such a challenge, and why layouts are slower than tucks.

You did really well though! I took intro to physics and AP physics, but I'm quite bad at explaining things. Someone in my class did her final project on gymnastics; mine however was on pole vault. Much simpler actually because it's only momentum and energy transfers, which are all a lot easier to deal with than center of mass, etc.

 

[gymluvr33]

The one thing you didn't mention, GT, was inertia, which is the summation of why a different body shape changes rotation. Inertia is why you turn faster when you pull your arms in, why that turn with leg above horizontal is such a challenge, and why layouts are slower than tucks.

You did really well though! I took intro to physics and AP physics, but I'm quite bad at explaining things. Someone in my class did her final project on gymnastics; mine however was on pole vault. Much simpler actually because it's only momentum and energy transfers, which are all a lot easier to deal with than center of mass, etc.

Ok, so let me see if I get this, inertia is basically a summary of center of mass plus radius plus angular momentum, etc. Is that anywhere close to being right? Sorry, I haven't taken Physics yet.

 

[NotAMom]

GL33, it's been a long time but let me try...

You are almost right but not quite. It's all about conservation of angular momentum. In simple form (and in a close system), angular momentum L in a given direction is a constant and it's defined as:
L=MVR
where M=mass, V=angular velocity in the same direction and R=radius from the center of rotation

Since M is a constant, V is inversely proportional to R. Therefore, the tighter you tuck, the faster you spin/turn/flip.

 

[tumblerK]

Here are some of the experiments we did in lab, they might help-

1. A person stands on a small rotating platform with their arms out and weights in their hands. Someone slowly starts to spin the person. When the person pulls their arms and the weights into their chest, they rotate faster.

2. Three rubber stoppers are placed at different radii along on a rotating platform. You spin the platform and slowly increase the speed. The rubber stopper farthest from the center flings off the platform first- and in a straight line.

I'll try to find the prelab power point that explains the physics behind everything and get it to you

 

[CoachTodd]

Here are some of the experiments we did in lab, they might help-

1. A person stands on a small rotating platform with their arms out and weights in their hands. Someone slowly starts to spin the person. When the person pulls their arms and the weights into their chest, they rotate faster.

2. Three rubber stoppers are placed at different radii along on a rotating platform. You spin the platform and slowly increase the speed. The rubber stopper farthest from the center flings off the platform first- and in a straight line.

I'll try to find the prelab power point that explains the physics behind everything and get it to you

Basically, in experiment 1, the speed of the weights in the persons hands actually never increases. It stays the same. The rotational speed of the person's center, however, increases to match the speed that the weights were moving when they were fully extended.
In a nut shell here is sort of what we are looking at.
If you have a rope with a weight on one end and you are holding the other end and you start to spin. If you have sections of the rope marked off we'll say in feet (heck let's make it a 10 foot rope and each foot is marked off on your rope)
While you are spinning, if you look at the first marked foot of rope, and if it takes you 1 second to spin around (to make calculations easy) that first mark on the rope is traveling at about 6.28 feet per second (2 X pi X radius)
The weight on the end of the rope that is at 10 feet is traveling at 62.8 feet per second (10 x as fast). If you could instantly pull the weight in without changing any angles, the center of the rotation would increase to match the outer most point of rotation (this is a conservation of energy thing)
Now, here is where I think some folks get a little confused. A tuck doesn't necessarily rotate any faster than a layout. It is just a smaller circle so it takes less time to rotate. Technically the center of mass is rotating at about the same speed.
Having said this, if the tumbler properly sets the tuck and starts to generate the angular momentum at the right time, when the tuck (after starting to rotate) the speed of the rotation in their center speeds up to match the speed of the parts that were pulled in.
I hope this doesn't over complicate what you are looking at. It's a little difficult for me to put it in words without equations and diagrams.

 

[NotAMom]

A tuck doesn't necessarily rotate any faster than a layout. It is just a smaller circle so it takes less time to rotate. Technically the center of mass is rotating at about the same speed.

CoachTodd, with all due respect, that is not true according to the basic laws of physics. The formula that I showed was watered down to illustrate to our young student. What it says is that for the same person the COM does rotate faster when it's moved towards the circle of the circlue.

 

[CoachTodd]

CoachTodd, with all due respect, that is not true according to the basic laws of physics. The formula that I showed was watered down to illustrate to our young student. What it says is that for the same person the COM does rotate faster when it's moved towards the circle of the circlue.

You need to look at the end of the post as well that says if you properly set the tuck (which is more of a laid out position) then tuck (pulling the outward weight into the center), it does speed up. Sorry if I didn't make that part clear.
One thing as well to note, a layout's center of rotation can be a bit different (i.e. I've seen many where the center of rotation is around the shoulders instead of around the waist) This makes if feel like it's moving even slower even though it may not be. Not really useful in the experiment but I just thought it was an interesting piece of information.

 

[Geoffrey Taucer]

One thing as well to note, a layout's center of rotation can be a bit different (i.e. I've seen many where the center of rotation is around the shoulders instead of around the waist)

The center of mass doesn't move to the shoulders, but you can sometimes create the illusion that it does if the CoM is moving in a parabola over the shoulders at such a speed where the shoulders or head appear to remain stationary. The shoulders don't actually become the center of mass, they just appear to because of the flight path of the actual center of mass (which remains around the waist).

 

[CoachTodd]

The center of mass doesn't move to the shoulders, but you can sometimes create the illusion that it does if the CoM is moving in a parabola over the shoulders at such a speed where the shoulders or head appear to remain stationary. The shoulders don't actually become the center of mass, they just appear to because of the flight path of the actual center of mass (which remains around the waist).

Reread it GT. Not the center of mass, the center of rotation.

 

[gymluvr33]

Thanks for everyone's replies. I got a little lost during some of the posts, but overall I think I understand this topic much better now.

TumblerK, I would love to see that powerpoint if you got a chance.

Thanks again.