Washington State Cheer-Sheet Analysis

This photo is of a Washington State Cheerleader performing a full basket. To perform this stunt, 3 or 4 bases interlock their arms while the flyer stands crouched down on their arms. The bases dip down then quickly raise their interlocked arms, which are a platform for the flyer, and throw the flyer as high as they can into the air in a straight line as the flyer stands up. She performs a skill when she feels weightless at the top of the throw. In this photo, you can see that she is twisting her body on two different axes, but I will only be talking about her twisting on the vertical axis. The picture was taken after she was tossed into the air, during her rotation. The bases at the bottom have their arms up throughout the whole stunt to catch her. This photo was taken at Washington State University by Paul Twibell during a football game in Fall 2017.

Stunting in cheerleading involves many physics concepts that allow for the stunt to be executed in a safe and visually appealing manner.

In this case, I will be talking about basket tosses. Extreme care needs to be taken for this stunt to be completed safely and successfully, meaning there are many rules and regulations set in place (AACCA, 2016). In fact, some competitions discourage them in routines due to the high rate of serious injury. The physics concepts that I will be explaining will involve the whole execution of the skill from the time the flyer is in their hands to the time that she is caught by her bases in a cradle. Concepts such as Newton’s first law will explain how they get her into the air. The use of torque will explain her rotation along with angular momentum. Finally, gravity explains her descent back towards the earth and the impulse momentum theorem describes the most critical part, the

catch.
The first concept that allows for this stunt to happen is the application of Newton’s 1st Law. This law states that an object that is at rest or is in motion will stay at that constant velocity unless a net force acts on it (Cutnell, et al., 2015). This is important in propelling the flyer into the air and the flyer coming back down. In the beginning of the stunt, the flyer is at rest in their hands. The net force that acts is the force applied by the bases that launch her into the air. This causes her to accelerate upwards until another force, the force of gravity, overcomes the acceleration upwards causing her to stop and accelerate back down to earth. The larger the force the bases apply to the flyer, the greater acceleration she will have and the higher she will go. The greater the mass of the flyer, the greater resistance she will have to the upward force and will result in the bases needing to apply more force to get the flyer into the air (Cavalier, 2015). This concept is vital in making sure there is enough height is the toss that allows for the flyer to perform the skill.
Another important physics concept utilized in cheerleading is torque. Torque is a measure of how much force must act on an object to cause it to rotate (Cutnell, et al., 2015). It is required for the flyer to spin as many times as she needs to before falling back to the ground. After being thrown into the air, the flyer starts with her arms up and her body is not rotating. When she reaches the peak of the throw, she will quickly pull her arms down and to the side of her body that will become her direction of rotation. The force created by her arms creates a torque that allows for the spinning motion. Her body must stay in line with her shoulders and hips in line throughout the rotation. The amount of force her arms apply will determine the speed in which she rotates. The net external torque from her arms can be calculated by multiplying her moment of inertia by her angular acceleration (Cutnell, et al., 2015).
In this photo, the cheerleader is twisting her body around, which involves angular momentum. Moment of inertia and angular velocity are involved in this equation. The moment of inertia is the ability of the object to resist rotational change and average angular velocity is angular displacement over time (Cutnell, et al., 2015). As you can see in the picture, her legs are together and her arms are close to her body. The moment of inertia decreases as she pulls her arms into her body and brings her feet together. Since her radius value is smaller, the distance from the center of her body to the outside of her body is minimized, and her mass is arranged closer to the axis of rotation (Cavalier, 2015). Having a small moment of inertia helps her in this case because she wants to minimize the resistance of rotation. The product of the moment of inertia and angular momentum is constant since there is no external torque during her spin. This means that when decreases her moment of inertia, she is also increasing her angular velocity. This allows her to complete her full turn before she returns down to her bases to be caught. If her arms were not pulled in tightly, her moment of inertia will be larger and her angular velocity will be slower. A slower angular velocity means she may not be able to complete the turn in the given amount of time and the stunt can become dangerous. After she has completed the rotation and is on her way down, she will put her arms out in a T and pike her legs to stop rotation. This will increase her moment of inertia, which decreases her angular velocity allowing her to come down in a position that her bases can catch her in.
The most critical part of the whole stunt is the catch. There are many ways that the catching of a flyer can end up getting everyone involved in the stunt injured. There are two important things to remember when catching a basket toss: catch high and bend with your knees. These two things relate to the physics concept of the impulse momentum theorem. This involves force and time as well as mass and velocity. The force is this equation is the force that the bases apply opposing the force the flyer applies due to her momentum. As she accelerates through the air downward, her momentum increases, which increases the force she will apply to her bases (Cavalier, 2015). The increased momentum can make the flyer come down very heavy and increases the force the bases have to apply in the opposite direction. The time comes in with the time it takes to catch. By starting with the bases having their arms high, they can make contact with her body when she is higher off the ground, which can help slow her momentum. By bending their knees to absorb the force, they are also increasing the time of the catch. It is important to increase the time of the catch because that reduces the amount of force that the bases must apply to bring the momentum to zero. Since mv ⃗=F ⃗∆t, the longer the amount of time, the smaller the force that needs to be applied (Cutnell, et al., 2015). When the time is increased for the catch, a smoother and safer stunt can be performed by all members involved. If the bases do not catch high or bend their knees, more force will be required to oppose her landing. This often leads to the bases leaning forward due to the extra weight and hitting each other’s faces, sometimes resulting in a broken or bloody nose.
The last important concept is the force due to gravity. Because she is being thrown into the air, gravity is acting on her and pulling her back down. At the peak of her height, her velocity in the y direction is zero (Cutnell, et al., 2015). As she comes back down, her velocity increases as she accelerates due to gravity. The flyer becomes a free-falling body and is caught at the bottom of the stunt by her bases. Gravity causes her to accelerate, subsequently increasing the flyer’s velocity. Her velocity is important in calculating her momentum, which is used in the impulse-momentum theory previously discussed. The force of gravity plays a role in her returning to the ground as well as in other physics concepts involved in basket tosses.
Cheerleading has significantly changed since its introduction in the 1880s. It has been closely associated with American football since its beginnings. Princeton University was the first school to form a pep club, which at the time was all male. Thomas Peebles, who was a graduate of Princeton, took the cheers to the University of Minnesota. Another student, Johnny Campbell, created a group of people to encourage the team and rally the crowd (Cheerleading, 2018). The hope was to, “inspire the home team and intimidate the opposition” (Hanson, 1995). This was the first example of organized cheer and they helped lead the team to victory. From there, cheerleading evolved into something more. Women were allowed to cheer for the first time in 1923 at the University of Minnesota. Cheerleading was thought of as an activity that required “minimal ability,” but soon tumbling and acrobatics were incorporated (Hanson, 1995). It continued to grow and add more elements. By the 1960s, cheerleading was in every high school across the country and was rapidly expanding. Over time, several associations have appeared to regulate cheerleading and create rules for the safety of everyone involved in cheerleading stunts (Hanson, 1995, AACCA, 2016).
Physics is critical for completing a basket toss safely. In fact, there are several studies that have been done on injuries in cheerleading. For example, a study done by Shields, et al. (2009), looked at the number of injuries due to various stunts, including basket tosses. It was found that 30.2% of injuries reported between June 5, 2006 and June 3, 2007 were due to basket tosses. There are many things that can go wrong in a basket toss and the risk of serious injury goes up because of the large heights that the flyer reaches during the stunt. Both a flyer and her bases can get hurt because of the increased time of falling that results in a greater velocity coming down. Because of this risk, there are a lot of safety measures put in place and a group must demonstrate competence in less difficult stunts before being allowed to try a basket toss. Cheerleading is full of physics that allow for stunts to be performed and each element is important. Although I specifically discussed a full basket, there are similarities in physics concepts between different baskets and stunting in general. In summary, in order for the basket toss to be completed safely and effectively, Newton’s 1st Law, torque, angular momentum, and the force of gravity are crucial concepts to consider.