In modeling instruction, practitioners talk about the “storyline” that we present. This morning I woke up and decided to attempt “stories” for AP1/CM (using the sequence from the AP1 Course and Exam Description). I tried to write them “student-friendly” without a lot of jargon, but of course some creeped in. Let me know what you think.

Unit 1: Kinematics

When we look carefully at the positions of objects moving in one dimension at equally-spaced moments in time, patterns emerge (two models: constant velocity and constant acceleration). We describe the patterns with different representations: words, graphs, equations (derived from the graphs), and other diagrams (motion maps or dot diagrams).

Unit 2: Dynamics

Now we turn from observing the two patterns/models to trying to explain their origins. We observe that objects interact with each other in several different ways. We model the effect of the interactions on an object as forces and observe that an object will maintain constant velocity with no net force exerted on it. When a constant net force is exerted, we observe constant acceleration motion. Since we have new ideas, new representations are needed (free-body diagrams, new mathematical representations, Newton’s Laws, the concept of systems).

Unit 3: Circular Motion and Gravitation

We extend the ideas from Dynamics (that interactions between objects may cause changes to the motion of an object or objects) to a third pattern, an object that moves in a circular path. We begin with an object moving at constant speed in a circular path due to a contact interaction(s), and then extend to objects that remain in a circular path solely due to a non-contact interaction (gravitation).

Unit 4: Energy

In Unit 2 we noticed that systems can change internally due to interactions within, or they can change due to external interactions. In this unit we go back to that idea and develop tools for comparing the initial state (“before”) to the final state (“after”) of an object or system. First we develop new quantities by examining how changes in the initial conditions of the system result in changes to the final state of a system. This leads to a very important principle: some quantities that can be calculated will remain the same total amount in the initial state as the final state, no matter how much change occurs within the system. Whenever this principle appears to be violated, we find that if we look carefully enough, we can see that it is actually correct. We keep our focus (relatively) narrow: the lens that we use in this unit is what happens when forces are exerted through a displacement. We examine many different systems, thinking qualitatively and quantitatively about their internal interactions and their interactions with external objects. More new representations result (new quantities, mathematical representations/equations, graphical representations (bar charts), and perhaps others).

Unit 5: Momentum

We begin by examining the quantity of motion that an object possesses. That quantity can be transferred to another object, and always maintains the same total amount, no matter what happens in the interaction. Again, we uncover an important principle about a different physical quantity that always remains the same and develop new representations. In Unit 4 we were concerned with the effect of interactions over a distance or displacement. In this unit we extend the observations about “quantity of motion” to examine changes to the initial and final state of a system or object with respect to the amount of time an interaction occurs.

Unit 6: Simple Harmonic Motion

We go back to observing motion, and note that some systems that have a particular back-and-forth quality to their motion (called simple harmonic motion) all share a unique aspect: a net force that is directed towards an equilibrium position and is proportional to the displacement of an object from the equilibrium position. We apply familiar techniques to the systems as well as develop new representations/models.

Unit 7: Rotation

We apply all the previous representations and models from linear (1-d) motion to objects/systems that change their angular position with respect to a coordinate axis.