Momentum Aerial at Science in the Park!
On the first day of fall semester, one of my youth students told me, “No one can disobey the laws of physics.” He is 100% right. While it seems like we are defying gravity when we dance in the air, we are really using those physical laws to our advantage - whether we know it or not!
We will explore some of the physics and physiological principles that help us dance in the air at Science in the Park on September 18, 2021 (10 am to 2 pm) at Wheeler Park. Come join us for presentations about friction, conservation of angular momentum, tension, and balance along with discussions of the vestibular system (dizziness!) and muscle alignment. We will have short, formal presentations at 10:25 am, 11:25 am, 12:25 pm, and 1:25 pm, and we will be at the booth through the entire event. Keep reading below for more information about some of the science that supports aerial arts (or just come see us on September 18!), and you can watch our (virtual) contribution to the 2020 Festival of Science.
Note - you can find more information about any of the physical principles described below by consulting a physics textbook!
Friction
Definition and Equations
Friction is a force that opposes an object’s motion (Fig. 1).
Friction in action! Momentum Aerial student Jade, uses friction to hold themselves up in the fabrics.
Fig. 1. Simplified “free body” diagram showing an object (the blue box) moving across a surface (a line). The object is moving because some force has been applied to it (pink line. Friction (the red arrow) is acting in the opposite direction to oppose this motion. The “Normal” force. The Normal force supports an object that is resting on another object -- it is (for example) the upward force that a floor exerts on us when we stand up. It is equivalent to the mass of the blue object. Gravity is the force that pulls us toward a body with a significantly larger mass (i.e., toward the center of the Earth). Note, the way this is drawn, all the forces are equal, so the object isn’t moving..
Friction is proportional to the “coefficient of friction” (μ - the Greek letter mu) which varies by material and the Normal force (N), which can be thought of as a supporting force: F=N. Different combinations of materials have different μ values. There are also different values of μ for static and kinetic (friction). Static friction is the force that you need to overcome to start an object’s motion. It is also the force that makes it possible to walk. Kinetic friction is the force you need to overcome to continue that motion at a constant rate. Kinetic friction works to slow down a sliding object. Static μ is bigger than kinetic μ for the same combinations of objects.
Friction and Aerial Arts
Friction underlies everything in aerial arts, so it’s pretty tricky to isolate moves that rely solely on friction. It’s easiest to think about friction on vertical apparatuses like the silks or rope. For example, every climb relies on friction to some extent. When climbing, gravity is working to pull us toward the center of the earth. However, we can position the silk or rope ways that result in an equal normal force (N; Fig. 2). For things like knee climbs, the material of your leggings ends up being pretty important with rougher material having a higher static μ.
Fig. 2. A happy aerialist (smiley face) takes advantage of friction (red arrow) to ascend the silks (yellow) while gravity acts to pull the aerialist to the ground. Friction is comprised of the normal (supporting) force of the fabric amplified by the coefficient of friction that takes into account the interactions between the aerialist’s hands and the apparatus. The aerialist also generates friction by squeezing the silks (applied force pointing inward).
Burning yourself while descending the silks (or doing a drop or just wearing shorts on a humid day) is due to kinetic friction. The molecules in the silk and your clothes or skin distort each other when they interact. That distortion ends up transforming kinetic energy into thermal energy. Ouch.
Conservation of Angular Momentum
Definition and Equations
Angular momentum is rotational momentum or a quantification of the amount of movement an object has around an axis of rotation: L=I. Where L is angular momentum, I is the “moment of inertia” and ω (the Greek letter omega) is the angular velocity (how fast the object is moving around its axis; the units are radians per second, but you can think of this as rotations per minute).
The moment of inertia (I) is the distribution of mass of an object about an axis. There are different equations to calculate this, depending on the shape of the object. The simplest textbook explanation is for a “point” object where I = mr2 (m = mass, r = radius from axis of rotation). For more complicated objects (like people), the equation for I is more complicated (it’s an integral), but the main idea is that this mass distribution is a function of the mass of the object and the object’s distance from the axis of rotation.
Angular momentum is “conserved,” which means that a spinning object will retain the same amount of spin unless it’s acted upon by some external force. That means that if an object has an angular velocity at time 1, then it will have the same angular velocity at time 2 (or 10 or 100) unless something external happens to change it. Changing something about the “moment of inertia” is NOT considered an external change.
The classic example of conservation of angular momentum is a spinning ice skater who changes arm position. When the ice skater starts spinning, they establish their amount of spin or angular momentum (L1). When they change their arm position, they change the radius (r) with respect to the axis of rotation. However, the angular momentum (L2) stays the same. If they pull their arms in, they decrease r, making I smaller, then angular velocity (ω) must increase because L1 = L2 by definition (it’s a law!).
Conservation of angular momentum and aerial arts
Conservation of angular momentum crops up every time you spin! Understanding how different positions affect your spin influence choreography choices.
You can easily change how fast you’re spinning by changing your radius. When we start learning about spinning in aerial classes, we usually do “tuck” and “layout” exercises where we start spinning and then change how small (tuck) or big (layout) we are by retracting or extending our limbs. Doing this affects our “radius” just like an ice skater!
In an ideal universe, we would just keep spinning forever, but we don’t live in an ideal universe. We change our angular momentum by introducing a little bit of wobble. There is also friction acting on the swivel that allows the apparatus to spin, so that friction also affects our angular momentum and eventually stops us.
Vestibular System
When aerialists spin, they get dizzy just like everyone else. But what is really going on in your body and brain when you get dizzy?When you move in any direction, including spinning, fluid deep in your ear flows past hair cells and sends this information to your brain to tell you what direction you’re moving.These signals are important so our body can subconsciously adjust our eyes, neck, and body position to stay upright when we move. Without our vestibular system, we would just fall over! We need this system, but why does it make us feel dizzy sometimes?
When you stop spinning, the fluid in your ear actually keeps moving. Just like if you were to spin a bottle of water and then stop, the water keeps going. Even though you’re not moving your brain and body are getting signals that you are moving! So your eyes and body will move to try and correct the mismatched signals. This results in a sense of dizziness that we talked about at the beginning of this presentation, falling over, and something we call nystagmus where your eyes twitch and dance around because they don’t know where they are in space. Nystagmus happens when you are spinning so fast your eyes can’t keep up. Picture following a train passing through downtown. If it’s moving fast enough you can keep moving your eyes back and forth to watch it. But if it was a really, really fast train your eyes wouldn’t be able to switch back and forth that fast and they end up having nystagmus. So how do aerialist spin without getting too dizzy? First of all, it takes practice! The more you do it, the less sensitive reaction your body has to that mismatched signal. Also, because we spin so fast sometimes it is hard to do what ballerinas and ice skaters do with spotting (or keeping your head mostly still while your body spins), so instead it can help to focus on one fixed point like the anchor point or a body part Finally, some people are actually able to train their eyes to move in the opposite direction of their spin to counteract the mismatched signals…but that is considered to be a very high level skill.
Muscles
A lot of the time the moves and tricks aerialists do look graceful and effortless, but it actually takes a lot of muscular strength to hold yourself in the air. As you train for aerial, it’s really important to use gradual progressions of strength and conditioning to get stronger so you don’t get injured and can stay safe in the air.Let’s take for example a straddle inversion. There are so many ways this move can be performed: with bent arms, with bent arms and bent legs, with straight arms and bent legs, or straight arms and straight legs. Each of these versions emphasize different muscle groups, or place demands on the muscles differently by changing the lever arm, the angle of pull, or the amount of stretch and fiber overlap in the muscle.
With a straight arm inversion - which is considered to be the most challenging strength-wise - you are using your knee extensor muscles like your quadriceps to keep your knees straight, your hip flexors and core muscles to bring your legs up, and your shoulder and elbow extensors like your lats and triceps to squeeze your body over your head from a very extended, or stretched out position. This can be very difficult since our muscles are like elastic bands. Your muscle fibers have an optimal length/tension relationship where they are strongest, but when your arms are over your head and your shoulder muscles are stretched out, they are beyond the optimal length/tension relationship for an easy, strong contraction making this move way harder with straight arms. In order to learn to complete this move, there are strength and conditioning progressions in place to get you to your goal safely and injury free. For example, you can change this move to make it a bit easier by bending your knees so your core and shoulders don’t have to work as hard since your legs are close to your body. Or you can bend your elbows so your shoulders are already by your sides instead of in an extended position. This position also allows you to compensate more by using your biceps muscles a bit as well. If you want to try this for yourself, try it on the ground! If you lie on your back and try and lift your straight legs in the air, and then you lie on your back and try and lift your legs when your knees are bent. Which feels easier? For most people, lifting your legs with bent knees will be easier, and a great way to train to progress until your muscles are strong and resilient enough to lift with straight legs.
Come to Science at the Park, Saturday, Sept 18th at Wheeler Park in downtown Flagstaff to learn more about the intersection between science and aerial arts!