One idea that has been gnawing away at me is Andy Rundquist’s awesome notion that, “Momentum is King.” One quick link to see some of his ideas in greater detail is here. My issue is how exactly to make that stick in a modeling class, or stated another way, how does the storyline for mechanics change? The main issue I’m going back and forth over is if you teach momentum before forces, when and how exactly do you introduce the concept/term force?

Here are my thoughts so far:

I’m planning to progress though Constant Velocity Particle Model and Constant Acceleration Model as set up by the modeling content. (As a brief aside, if your not familiar with Kelly O’Sheas blog on modeling, go there ASAP!) From there, I’m planning to use a modified version of the Momentum Transfer Unit (Impulsive Force Model). After that is where I’m stuck, but here’s what I’m roughly thinking:

1) Jump to Balanced Forces, and don’t make the explicit connection between momentum transfer and forces. Basically begin creating a second parallel concept. Progress through the modeling materials for balanced forces (Free Particle Model is the official name) as designed and wait until unbalanced forces (Constant Force Model) to make the connection.

2) Recast the balanced forces model as multiple transfers model and remove the discussion of forces. Continue to reinforce the idea of momentum swaps, but now discuss the fact that the swaps can balance out. Focus on the system schema and stress that if there is not net momentum swap, the momentum must stay constant. Instead of hammering home “no net force, no acceleration; net force, acceleration” recast it through momentum. Then introduce the concept of force in the next unit, Unbalanced Forces Particle Model (which may or may not need/get a new name)

3) Jump to Unbalanced forces first and show the connection between impulse and Force. Begin by showing that a force is the rate of momentum change and that the area of a F vs t graph. You could build the IF bar graphs in the momentum unit into IFF bar graphs. In the process focus on how each object has the same momentum swap, but different accelerations; that the forces are the same, but the effects may be different. (I’m looking at you bug on windshield problems!). Once complete, go to balanced forces and show that you can have multiple, simultaneous interactions, which can balance out. Now bring in things like system schemas and force diagrams.

My quick $0.02:

1) If I’m making the effort to put momentum first, it doesn’t seem right to then ignore it when introducing the concept of forces.

2) Seems to flow a little better than (1), but when do you build in force diagrams? Adding them in the unbalanced forces unit make that unit really big, but I’m not sure I would feel right calling them momentum swap diagrams (especially if no other physicists do so).

3) Part of me is really drawn to this storyline, but in the end, that means I’m teaching Newton’s Law in the reverse order (3rd -> 2nd -> 1st). There is probably a good reason why no textbook or the modeling materials do it that way.

I’d love to hear feedback, if you’ve got any.

For me the problem is energy. It’s so useful for doing all kinds of problems, but I don’t feel it’s strictly necessary. However, continuing to say “you’re swapping momentum at a rate dependent on how close you are” is a real pain compared to “you’re cashing in potential energy.” What I’m really not sure about is whether this is a philosophical question (do we really need both momentum and kinetic energy to describe motion) or a pedagogical one (should we teach just one of them).

I’m guessing ill do energy after forces as a way to ties it all together and bring in elastic vs inelastic collisions (which I’m skipping in the earlier momentum unit.

I like the storyline (well, generally – see below), but… I think that it requires some knowledge and perspective to appreciate, so it’s the kind of unification that I save for the second year. I go motion/forces/UCM/grav/momentum/energy/oscillation/electricity, and the biggest unities that I’m going for are that CPVM/BFPM are special cases of CAPM/UFPM, the momentum principle (explaining conservation of p and impulse), the idea that conservation of p is the same as Newton’s 1st, and the energy principle (explaining work and conservation of E). In the second year, we go for the more holistic view of kinematics, circular motion, momentum cons. and transfer, and oscillations as being all a single underlying model, but I don’t think that they have the perspective the first time through to appreciate it.

The biggest unity in the second year, BTW is Noether’s theorem; once we’ve recast everything from the first year (and more) in terms of the p, E, and L principles (only), those are just three results of Noether’s theorem, so the whole two years is really just one concept. 🙂

Thanks for the input!