Conservation of angular momentum: Toes to Bar (TTB)

In physics, angular momentum (in simple terms) is the product of mass of an object (m), the distance of the object from the center of rotation (r) and the tangential velocity of the object (v):

L = m * r * v

Angular momentum is conserved unless there is external torque (force). In other words, m, r or v can change, but L will stay the same. Therefore when you decrease the radius of a rotating object, the velocity must increase to conserve angular momentum. If this doesn’t make sense, don’t worry, just trust me. This is why when a gymnast tucks their legs, they rotate faster and when a skater pulls their arms in, they spin faster.

So what does this have to do with CrossFit? Everything. Moving your body in space requires that you operate within the laws of physics; thus it is beneficial to know what the rules are. Let’s take toes-to-bar (TTB) for instance. When we “kip” (or arch and hollow in a pendular fashion) to do a TTB, we all know from experience that bending our knee joint makes our legs seem to go up easier. That is because you are decreasing the radius of our legs (r). Since angular momentum (L) is conserved and the mass of our legs (m) is constant, the velocity of our legs increases. So bent legs is better right? Only if you do it the right way.

From the back swing (or arch) you have two forces working in your favor 1) gravity and 2) your body’s natural elastic recoil. At this point, gravity, the elasticity of your muscles/tendons/ligaments, as well as whatever contractile forces of torso and shoulder flexion you apply all accelerate your body from zero velocity at the full backswing to whatever velocity you reach at the bottom of the swing. Since passive forces (gravity and elasticity) that don’t require your own ATP are helping you gain momentum, it is to your distinct advantage to keep your legs straight. Then after the bottom of the swing you have zero elastic recoil to use and gravity is working AGAINST you. Therefore to resist the force of gravity, if you bend your legs you will increase your velocity since the momentum you have stored up is conserved. Then your toes touch the bar and what happens then? You start to fall into the back swing and you have gravity working for you again. So you want STRAIGHT legs again. This allows you to build up more momentum in the back swing so that you can arch deeper. A deeper arch = more potential for elastic recoil and gravity to help the next front swing = you have to use less muscle.

Although this is a very simplified form of physics as this is not a true fixed axis rotation, I would contend that the optimal body form is… OK HERE IS THE POINT FOR ALL OF YOU GETTING A HEADACHE…

Straight legs and deep arch with shoulders in front of the bar, forward swing and accelerate with straight legs until through bottom of swing (hanging vertical), then bend legs as they come up until they touch the bar, then straighten them again as they fall back down into the straight leg deep arch again.

That being said, this is generally not what I do. Unless I am doing more than 30-40 TTB in a row and my abs aren’t fatigued, I find it easier to just do long straight leg swings inhaling deeply in the back swing and exhaling deeply in the front swing. I find that with a very deep arch the acceleration provided makes the TTB so easy that the knee-bend isn’t necessary for me (and thinking about the bending then straightening keeps me from relaxing through the motion). TTB are a little slower this way, but much, much easier. If my abs get fatigued then I bend my knees as above.

My rule of thumb is that if you can’t hold a conversation while you are doing TTB then you are probably working too hard and not taking advantage of your swing and physics.