Unit Summary and Shifts
In a nutshell, this is what my momentum unit looks like:
- Discover impulse
- Work quantitatively with impulse
- Multiple representations
- Using impulse to define conservation
Teaching Momentum, an Introduction
A quick review of my teaching values before we begin. See the introduction for more.
- Any student can learn physics, and curiosity about the physics world around us is an innate attribute of humanity.
- Intuition can be a powerful tool to co-construct knowledge
- Order matters. Language matters.
- Shut Up and Listen
- EVERYTHING is an opportunity for an experiment
- My primary responsibility is to ensure a safe space for students to learn
When I was taught momentum it looked something like this:
- define momentum as mass x velocity.
- Talk about how to change momentum through impulse
- Revisit action-reaction pairs. Throw an egg into a bedsheet.
- Define conservation of momentum as initial = final. Solve collision problems accordingly.
In my experience there was also no mention or use of various graphs. When I started teaching I was able to get a hold of the entire curricular materials from a prestigious, high achieving, highly affluent school in the area. They taught the sequence very much the same way. Obviously this was the “best” way to teach momentum… right?
Over the years through a combination of teaching the AP curriculum, exposure to the ISLE method of learning and the modeling curriculum, this sequence has shifted dramatically. I have aligned many of my routines with these two models. However, my structure for teaching momentum is not the same order as ISLE or modeling. In both of those curricula, students are first tasked with discovering conservation through a series of experiments to kick off the unit. My order is slightly different.
One of the critical choices I make about momentum is to teach it before energy and after forces. I do this because change in momentum is a natural consequence of an object experiencing a force. Momentum is really just forces repackaged! I don’t want students to discover conservation first, because I want them to think about the processes during the collision first, then we can apply those to different scenarios.
I was super excited to find out recently this has actually been studied. You can read the article here, but here’s the Tl;Dr –when students are taught from big idea down, they learn the material better, making more connections, and this study was specifically done with a framework for momentum. (See the framework below)
Momentum is a huge, critical unit, so I’m going to break this down into three separate posts. This first one will take a look at impulse. The second post will be a short explanation of two activities I do, one for regular students and one for AP. The last post will discuss conservation. I want to note that I do not plan on including every detail, activity and problem set in these posts, only the ones I think have substantial value to you, the reader, and those that constitute major shifts in my teaching over time.
One thing that remained true, even in the very first years of teaching was my attempts at emphasizing that momentum is not something new, it is simply forces repackaged. The other statement I would make often is that the impulse-change in momentum relationship is two ways of saying the same thing. Like “Hi” and “Hello.” Yet, these ideas were not sticking in students minds. Furthermore, I was fully aware that students were making no connections between impulse and conservation. How do we get students to understand these ideas with full integrity?
The realization for me came after a vocabulary shift: rather than defining a force as a push or pul we now explicitly define a force as an interaction between objects. This definition became the driving force for my reframing of momentum.
Please don’t steal for profit on TPT. That harms the teachers who share, those who are in need, and our profession as a whole.
Observational Experiment: We begin with an old demonstration from earlier in the year: our lovely bowling ball friend. We are already familiar with the fact that an unbalanced force will cause the ball to accelerate from the forces unit. I ask a student to give the bowling ball the hardest whack they can with a hammer. Unsurprisingly, the ball barely moves. But the force was so strong! What can we do instead? Well, if we tap the ball repeatedly, then it will begin to accelerate. This is how we first define the impulse-change in momentum relationship. We need a force exerted for a certain amount of time in order to change an object’s velocity. We do not define this yet as a formal equation, but we recognize that force and time must be multiplied. To define momentum itself I do a live google news search for the word momentum. The headlines are always sports, politics and stocks. We talk about what the word means in those contexts. We typically arrive at something like “having a lot of momentum means hard to stop” and then we formally define it as mass times velocity. I’ve never been one to do elaborate day plus activities to define simple terms when we can use their lay knowledge as a foundation for their scientific definitions. At least for something like this. We have much more important work I’d rather spend that precious time on. This is important as we move to the next phase. My students hear from me frequently: whenever you get a graph your first question should be does the slope tell me anything (division) does the area tell me anything (multiplication).
Quantitative Experiment: I have run this lab two ways, but the idea is the same: have students quantitatively compare impulse and momentum change. The original way I performed this lab was to affix a force probe to the track, then run a car into it with the pistton out. The piston allows the time frame of impact to extend so students can see the curve. A motion sensor is set up on the opposite end so students can obtain velocity values. When we open class I have sketches of the graphs they will see and I asked them how they could determine impulse and momentum change from the graphs. Students are asked to sketch the graphs, determine the change in momentum and determine the impulse by using the software to take the area under the curve. In a newer iteration of this activity I use the iOLab to the same effect. Students run the iOLab into a wall or textbook and analyze the same data. I ask students to determine the relationship between impulse and momentum change. Then I ask them to write that relationship down and rearrange the equation until they get something they recognize.
Recap and Multiple Representations – We will recap yesterdays activity through a discussion and whiteboard presentations. By the time we finish students recognize that the impulse-momentum relationship is just F = ma rearranged. This is where I emphasize again we are not really doing anything new. The next thing I ask them to do is to imagine the force probe/wall (depending on the iteration of the lab) was replaced with a second car of equal mass…what would the force graphs look like for each car? We are, in effect, previewing the law of conservation. If we go back to the definition of force: a force is an interaction between objects, then it follows that the force on object 1 must be equal and opposite to the force on object 2. The time must be the same. Therefore, the impulse is equal and opposite. While we could easily jump into conservation laws from here, we continue working with representations focusing on impulse and momentum change.
In a whiteboarding exercise I provide students with several scenarios. In each scenario I have provided one representation. Students are asked to create the other 4 representations. The purpose of this is to ensure they are accessing everything they have learned already. This is, in some ways, I type of interleaved practice since they are pulling from the whole year.
One Final Problem Solving Example
Over the next few days we continue our practice with an emphasis on multiple representations, graphing and the fact that an impulse causes a momentum change and that they are one and the same. One of my favorite questions is the following one.
Identical forces push two different pucks the same distance. Puck A has four times the mass of puck B. Which experiences the greater change in momentum?
Can you describe what student responses look like? They come in three levels.
Level 1: Puck A will have the greater change in momentum because it is bigger. More mass means more momentum. These students have missed the point completely. They are focusing on formulas and completely disregarded the velocity piece. While “puck A” is the correct answer, I cannot give credit for this response.
Level 2: These students make some attempt to determine the velocity but end up writing a lot of circular statements and attempting a lot of calculations. Some of them get there, but this process is long and arduous!
Level 3: These students correctly recognize that since impulse and momentum change are the same thing, they can easily look at the impulse to determine the answer. The force is the same, but the mass is different, resulting in puk A taking longer to get to the finish line, therefore puck A is greatest.
I LOVE this problem so much. It’s a fantastic example of why expert-level thinking is so important for students learning physics. Students see the word “momentum” and they want to do p=mv. While you could do this, it takes a long time to get to the answer. If, instead, you take a step back and recall that impulse and change in momentum are the same, you see that you only have to figure out what is going on with time, since the force is the same. This piece is a lot more intuitive than determining the final velocities of each puck. I have used this as a warm up and as a quiz item.
We also take advantage of the AP question bank and we will begin probing the idea of what it means for an impulse to be external vs internal. This falls in line with previous experiences related to defining forces and systems and serves as a good launch point for conservation of momentum.
Scaling Up and Down
Regular physics generally gets all of the same structure materials as AP minus the AP practice FRQs. I will, however, spend a little less time on multiple representations and a little more time on calculations for the sake of “easy wins” so students can gain some confidence.
AP Physics C: My students in this course have all taken APP1. We instead have a “momentum mastery” project, a quick 2D lab and AP FRQ practice.