Are you looking at STEM colleges? Considering a career in science or engineering? Or are you just wondering how physics could apply to the so-called real world? All of these come together at the Olympics.
Like many of you, The Stemwinder has been watching the Rio Summer Olympics. In addition to the dazzling feats of human endurance, skill, and perseverance, the Olympics are a great time to look for real-world applications of engineering, math, and physics. Today’s post will deconstruct some of the STEM principles which are harnessed by world-class athletes in pursuit of Olympic gold.
An athlete named Simone Biles has won five medals, including gold in the Women’s Vault. As you watch her winning vault, the first step is for her to develop momentum by running full-speed towards the launch site. Why is that momentum important? As you will learn in a freshman Physics class, momentum for a given mass (in Simone’s case, about 48 kg) is created by the product of mass and velocity. The run-up creates the momentum used during the launch and initial turn – once Simone leaves the ground, she has a fixed amount of momentum which she can then apply in different directions to perform flips and spins.
Well, that momentum is actually a vector quantity, just like velocity. And it comes in two flavors: Linear momentum and angular momentum. These combine to determine what Simone’s body will do in free space and as it interacts with the launch springboard, vault, and landing pad. Momentum affects many other Olympic athletes in their sports, so it is important to understand the application of linear and angular momentum using the Women’s Vault as our instructive example.
Mathematically:
The momentum of a mass 
traveling with velocity 
in a straight line is given by
while the angular momentum of a point-mass rotating along a circle of radius 
at 
rad/s is given by
where 
. The tangential speed of the mass along the circle of radius is given by
Expressing the angular momentum 
in terms of gives
Thus, the angular momentum 
is times the linear momentum. Linear momentum can be viewed as a renormalized special case of angular momentum in which the radius of rotation goes to infinity.
In linear motion, momentum is created by a force acting on a mass in a single vector direction, which produces a velocity vector. For angular momentum, that force acts in a circle of radius r and the force is called torque. You can think of torque as the “twist” to make something go around in a circle: a doorknob, bottle cap, or screwdriver. Torque τ is shown in the following animation as the force F which accelerates rotation at radius r and then stops and reverses it:
How does Simone harness these physical laws and formulas to perform her gold-medal winning vault? Watch again, paying attention to the changes in her rotation. At the end of her run-in, she applies torque with her feet to generate a rotational force. Her body – arms and legs outstretched – begins to rotate. After leaving the vault, you can see her arms tucked in closer as she torques her body to generate a twist along with a spin – then she extends her arms at the landing to slow her rotation – widening the radius and, mathematically conserving momentum, lowering the speed of rotation.
Applications in STEM education:
By now I’m sure you’re wondering how this applies to your choice of major and desire to pursue a STEM education. Conservation of momentum, and the motion of bodies (gymnastic or otherwise), is useful in any technology that has a physical-mechanical interface with nature. Consider, for example, wind-generated electricity: turbines extract energy from wind moving linearly, convert it into rotational force, and turn a generator. Future posts will discuss wind power and other forms of renewable energy – but for now you only need to visualize the similarity between Simone Biles’ rotating body and a modern multi-megawatt wind turbine.
Getty Images – Bryn Lenno
Another application of linear and angular momentum shows up in the Olympic sport of velodrome bicycle racing.
Why does a bicycle not fall over while you’re riding it? It is not because the rider is actively controlling the handlebars to keep it upright, but rather because the angular momentum of the two rotating wheels actually creates a force that tries to keep the bike upright. Here we can see Prof. Walter Lewin at the Massachusetts Institute of Technology demonstrating the practical effects of the gyroscopic effect of a rotating bicycle wheel:
Professor Lewin is demonstrating the practical application of the gyroscopic force, which is created by a mass rotating around an axis and produces a force normal to the axis of rotation. Where does this force come from? As you can see in the video, he inputs angular momentum by setting the wheel in rotation.
In this drawing you can see a force created by the rotation of the wheel around the spin axis acting on the gyroscope in this drawing. Recall our previous description of how torque created angular momentum. Conservation of angular momentum means the spin axis will try to stay in the same horizontal plane, and you can see how Professor Lewin has to push the rotating wheel to get it where he wants it. None of the cyclists in the Olympic velodrome have to think about this or do any vector mechanics calculations in their heads; the forces exist and the Olympians harness them as part of their sport. How does this apply to a STEM curriculum? Gyroscopic effects occur in many physical systems, from the forces acting on a jet engine turbine to the tiny but not insignificant forces in a rotating disk drive.
So while you’re watching the Rio Olympics and you see gymnasts flipping and cyclists spinning, remember that mastery of these and many sports requires the talent to feel and overcome the forces generated by angular momentum. How many Olympic sports can you spot that require this mastery?