I taught college freshman physics for one year, plus six years of FRC mentoring (and a significant number of informal courses within my workplace, ranging from *nix shell scripting to geographic projections). What you have here appears to be good stuff, but I suggest turning it “inside out”. Here, Robotics is the inspiration, so I suggest starting with practical FRC problems and turning that into what the class delivers. That is, start with a problem. E.G. Why did my robot fall over when my top heavy robot accellerated or turned too quickly? Use that question to show how low the CoG must be to keep the robot upright. Lots of other cases - how do I get across the field quickly? Why is this robot so sluggish?
On the cross product, I usually like to show this with the second vector beginning at the END of the first, rather than having a common origin. This has two great advantages: in explaining torque, it is physically what is going on - 𝜏=rxF means that torque at the origin of r when F is applied at the end of r. It also makes the right hand rule easier to visualize: line up your right palm with r and bend your fingers towards the palm to align with F, torque is the direction of your raised thumb. Second, (once combined with the right hand rule), it is clearer that axb=-bxa. Later: more like the pics on slides 9 and 10. I also like to make it clear that the right hand rule is a convention rather than reality; If you were to use the left hand rule consistently, physics would work out the same (at FRC scale, anyway).
General order of presentation: I like to start with things that are well understood by most people and then moving to things fuzzily understood, and finally into those which most people are clueless or have misunderstanding: Start with distance and time* then speed and acceleration [and maybe jerk]. Then mass vs force [Newton’s laws here], followed by work [where you start out with motion and force in the same direction, then antiparallel, and finally generalize to the dot product], energy, and power. So far, everything can be point masses. Only then add angular distance, speed, acceleration, torque [cross product here], and the free body diagram.
Before getting into gears and belts and chains, cover levers. Go back to torque, then point out how useful a lever is, and finally explain these are specialized applications of the lever.
I’ve taken the “iterative design process” (engineering process) to a separate presentation. My best experience teaching the engineering process to young people has been to start with “What is the difference between science and engineering?” (tabloid answer: science asks why things happen like they do, engineering figures out how to solve a problem.) Then, cover the scientific process (which is a review for most high school students) and why it works for science. Then, consider engineering, how it’s different, and why the same process would not apply. Then, show how important it is to define the problem before designing a candidate solution, and then get into build, test, and iterate. THEN, get into strategic analysis - what are the strategic costs/benefits of a certain action (example, raising the elevator holding a game piece) takes 10 seconds, 5 seconds, 2 seconds, 1 second, half a second , or a fifth of a second? What’s the benefit of a 99%/95%/90%/80%/65%/50% reliable intake?
* OK, it turns out no one understands time, but the intuitive understanding of time works pretty well until you hit relativistic or quantum effects. Outside of designing the deep intermals of control electronics,I can’t think of any case where this has mattered in an FRC game so far.
Your students will be better off having this intro, and then being given an opportunity to do related hands-on activities, than they would be without it.
