If we model the Flying Pig as a planet and the force of gravity as coming from the sun, we can use the Flying Pig to illustrate all three of Kepler’s Laws of Motion. Through observation or analysis, the Pig can be shown to move in an elliptical orbit (with a very small eccentricity), sweep out equal areas in each interval of its motion, and one could even tie the string to be shorter and show how that results in a shorter period to help bring intuition to Kepler’s 3rd Law.

In Astronomy, you can also use the Pig to talk about orbits and conic sections (circles, ellipses, parabolas, and hyperbolas, i.e., all the possible types of motion given a central force). Give the pig a little push and a little speed with the wings off, and it moves in a little circle. Ask your students, “What would the pig have to do to move to a larger orbit?” (Bigger push=more speed). A really fun question to explore with your class is the Hohmann Transfer. Have the Pig flapping and ask your class, “How would I have to push on the pig to move it to a larger orbit?” It makes for a really fun experiment to have the kids try pushing on the pig in different ways to learn that thrust, i.e., simply speeding up the pig, is all that is needed to transfer to a larger orbital radius.

I find the biggest hurdle is teaching that centripetal forces are not “new” forces, that anything can act as a centripetal force if an object is moving in a circle. I always try to teach Newton’s 1st Law as “An object will move at a constant velocity unless unbalanced forces act on it.” The Flying Pig is perfect for this model because something has to be happening for its velocity/momentum to be continuously changing. The Flying Pig is also a great tool to utilize in the Energy unit when modeling energy transfer. Some ideas to incorporate are:

● “Where does the Flying Pig get its Kinetic Energy from?”
● “Draw an Energy Bar Chart of the Pig while being held stationary at an angle and while moving.”

I first use the Flying Pig in this class when teaching kinematics at the beginning of the year. A very simple, short experiment is to ask, How fast is the pig moving? I enjoy doing this as an open whiteboard experiment, because I notice that when I merely tell students about the kinematics of circular motion, they tend to forget that the distance the pig moves is the circumference of the circle it traverses. When presented as a more open-ended experiment, the students can reason it out themselves, and that has tended to result in deeper understanding and longer-lasting impact.

A great follow-up to this lab is to ask, “OK, now how fast are WE moving? (I’ll leave it up to you and your reference frame to decide how deep you want to go down the rabbit hole with this one, but I usually stop with the approximate speed of our sun orbiting the Milky Way).

One of the most important parts of teaching this level of physics is teaching the balanced vs. unbalanced forces models and their corresponding motion. In addition to everything I do in conceptual physics with the pig, a great additional use of the pig is to use it as an accelerometer. One of my favorite balanced vs. unbalanced forces problems is modeling the motion of a sprinter during a 100m dash or a car driving a mile as fast as it can go. It is a great way to combine the models of balanced and unbalanced forces, along with the corresponding motion graphs. By simply holding the pig from the string while you speed up, slow down, and walk at a constant speed, you can help students build a deeper intuition of Newton’s 2nd Law.

Civil Engineering:

Just like how our pig “knows” what speed to travel safely in its circle, civil engineers place yellow signs to give the recommended speed to go around a curve. I start this activity by using the exact lab provided by Arbor Science (see the PDF of the lab here, along with the corresponding teacher notes here) to teach about centripetal forces and tension. Side note: This is a great lab that I think is perfect at this level because of how it connects kinematics, free-body diagrams, and centripetal forces.

The follow-up I do on the next day is to have students use Google Maps to find a curve that they can also see real-life pictures of by dropping the “little man” on the road. We then calculate what the sign should say by saying that friction must be acting on the centripetal force, pulling the car around the curve (if a student asks why it’s friction, ask what would happen if the curve were covered in ice!). By using something like MS Paint or anything that can make a circle, you can fit a circle to the curve and measure the radius of the curve. You then have to assume a coefficient of friction, which leads to a great talk about engineering (should an engineer choose a coefficient for the best possible conditions, like a hot and dry day, or the worst possible conditions. In upstate NY, where I teach, I use μ=0.2 as that seems to approximate our road signs for rubber on an icy road. This is a phun way to connect our classic pig experiment with a real-life calculation.
The next follow-up in the AP Physics 1 class would be to talk about banked curves. I like doing this activity right after the classic pig lab because, just like how the mass term cancels out when you solve for the equation of motion for the pig, an extremely similar line of thought is used for the banked curves equation. This allows for natural scaffolding that makes the banked curve problem substantially more approachable.

Artificial Gravity and G-Forces:

I always like to ask my class, “What do you think the pig feels while spinning in its circle?” The Flying Pig is the perfect tool to have on hand when talking about artificial gravity (like in the Gravitron Ride at fairs or as heavily discussed in the book/upcoming movie Project Hail Mary by Andy Weir). Calculate the centripetal acceleration of your pig after performing the provided lab, and then ask some questions like:

● How fast would the pig have to move to produce a gravity of 1-g?

● Calculate the centripetal acceleration of a ride using data from a video and compare it to the Pig's and Earth’s gravity.

● What would happen if a fighter pilot took a turn with too small a radius of curvature? (This is called G-Lock and happens when the g-forces are so high that a person blacks out. There are a lot of really cool biology connections here, as everyone has a different tolerance of g-forces, as well as things like how using breathing techniques and a pressurized G-suit can help a pilot handle larger accelerations.

● Talk about astronauts and centrifuges used for training. Our little pig is like its own little centrifuge. 

I will additionally use the Flying Pig in my Simple Harmonic Motion Unit because the Flying Pig is a conical pendulum. As is done in the course, the small angle approximation is used to classically show that a simple pendulum is not true simple harmonic motion, but is simple harmonic motion in the case of small angles (I always say less than 30° because all things considered it gives less than a ~5% error). Likewise, we can use the small-angle approximation on the Flying Pig and see how the measured period of the pig compares with the theoretical period of a simple pendulum.

Instead of doing the classic Flying Pig Lab (linked again here), I prefer to ask the students to predict the period of the Flying Pig, starting with a free-body diagram. Finally, at this level, it is great to see when a model breaks down and why. In the Flying Pig lab, the mass terms in the derived equations cancel out, showing that mass should have no effect on the period and angle of the pig. In experimentation, though, we see that the pig does, in fact, travel in a circle with a smaller angle (and the same period) when something as small as 1 pig mass (approx. 200-300g) is added to it. This is because the motor has a fixed power output, so the pig is no longer able to maintain the same angular velocity.