# Peer Instruction Fail

**Posted:**September 20, 2011

**Filed under:**Introductory Mechanics 6 Comments

*(This is not a criticism of Peer Instruction. It is just a tale of one of those times where the right idea failed to gain traction*)

Yesterday we tackled a classic parabolic motion conceptual question in class, “three ships”, shown below.

They answered this question in their pre-class “reading” (actually I’m using smartPhysics so they watched a multimedia presentation). I am teaching two sections (35 students each) and will just combine their data here. On the first in-class vote, they were 51% correct. After discussion (5 minutes in one section, just about 10 minutes in the other), they revoted and were only 59% correct, which is a learning gain of 0.16 for those who like to use learning gains on clicker questions.

And the discussion was super animated. It seemed like it was so productive, but I guess it was really more about the two sides (B vs. C) digging their heels in.

And this does happen on occasion with Peer Instruction. You see 50% correct on the initial vote and smile to yourself thinking that the subsequent peer discussions is going to be a good one, but then sometimes the number of correct answers barely budges on the revote.

In the case of this question, it seems like I need some scaffolding clicker questions or other activities leading up to this question. Perhaps this scaffolding won’t improve the initial vote, but will perhaps give them more points of reference and examples to use in their discussions, helping the peer instruction really do its job.

Before coming to this question we spent 20-30 minutes developing position and velocity graphs in the horizontal and vertical directions starting from a motion diagram of a basketball shot, but did not talk explicitly about time at all during the sequence. Then we discussed the clicker question for the horizontal projectile vs ball drop demo and they were nearly unanimous in getting that question correct. But it seems like more scaffolding is still in order.

# Walking the interactive classroom walk right out of the gate

**Posted:**August 12, 2011

**Filed under:**First day of class, Introductory Mechanics 10 Comments

*Executive summary: This year I’m going to get my intro mechanics students to make motion **diagrams and we are going to play “match the graph” games with motion detectors on the first day of class. This is going to happen instead of me spending the whole class period telling them how the course is going to work and then actually starting in with an interactive classroom on day 2. How novel!*

### First day of classes = kind of awkward

One thing that has bugged me about my courses over the past couple of years is that my first class ends up being a mostly administrative/logistical introduction to the course, with lots of salesmanship and my regular level of being silly on top. I spend most of the time that day talking and there is a huge disconnect since what I’m talking about is all the ways that they are going to learn that don’t involve me talking. Yuck!

Part of why I do it this way is because I am a big advocate of pre-class assignments/some sort of flipping of my classroom (using reading assignments, screencasts or other multimedia). I have touched on these things before (here and here). In terms of consistency, it seems inappropriate to stomp around telling them that I want them to ALWAYS come to class prepared to build on the concepts from their pre-class assignments, and then start trying to teach them Section 1.1 on the first day outside of my regular flipped framework.

But in terms of an interactive classroom, day 1 is me talking the talk, but not walking the walk.

### My new plan is to jump right in

But this morning I decided I’m going to change it up this year. I’m going to introduce myself, tell them that I (heart) the interactive classroom and jump right into something fun and learningful (I’m allowed to make up these types of words).

### I think they think the students are supposed to show up already having a physical feel for motion

Most introductory physics textbooks jump into 1D motion right away, perhaps with a preceding chapter on units, vectors and other physics-support stuff. But what they don’t do is try to spend some time helping the students develop a feel for motion. Perhaps students can quickly go from from an x-t graph to a v-t graph, but have they developed a physical sense of what sort of motion something is undergoing if they see a parabolic v-t graph? Knight does a decent job of some of this. He spends time on making motion diagrams (the picture that you be created if the moving object dropped a breadcrumb once per second, similar to a strobe image). But it is ultimately up to the students to develop a physics sense of these motion quantities and how they interact with each other, and most textbooks don’t even try set the students up to do this; they just treat this physical sense as developed from the get-go. By the way, I am using smartPhysics as my text this year (as I discuss here) and their text is no different in this way.

It is interesting that, under my new plan, it is almost better that the textbook doesn’t try to help the students develop this physical sense of motion. That means that I can jump right into some “developing a physical sense of motion” activities on day 1 without undermining my usual structure of doing some learning from the text before class and then coming to class to refine and build on that learning. Thanks textbooks.

### The actual jump right in activities I am mulling over

**Motion diagrams** – The first thing I am going to do is to walk across the front of the room at constant velocity, saying “now”, once per second and ask them to whiteboad a picture that represents where I was each time I said now. Then through some combination of whiteboarding, clicker questions and me running around at the front rhythmically shouting “now” we explore what the motion diagrams look like if I am speeding up, slowing down, going in one direction vs. the other or just standing still. In the middle of all of this I can introduce the idea that velocity can be represented by an arrow drawn from one dot on the motion diagram to the next. Perhaps Dan Meyer’s WCYDWT basketball shot will make an appearance.

**Games with motion detectors** – This is super fun and a great way to help students develop a physical feel for all the motion quantities and how they are related. Put them in front of a motion detector and give them an x-t, v-t or a-t graph and ask them to move their bodies to reproduce that graph. Through this process they get to relate their own physical motion to all three graphs and how they are related. *Note that I have never actually done this in my own classes, but have done it as a participant at a workshop and loved it!*

### Generating buy-in by walking the walk

I believe that generating student buy-in is the single most important factor in running a successful interactive classroom. And jumping them right into whiteboarding and learningful clicker questions (instead of starting with “what is your major” clicker questions) seems like it can only help to generate buy-in.

Since I usually spend an entire class period talking to them about the course structure, there must still be a bunch of stuff that I need to communicate to them early in the course, if not on day one. And this is very true. I’m just not going to front load it. What I am now planning on the first day is not going to show up on their first homework assignment (partially true, they probably will have to translate between x-t, v-t and a-t graphs), so I can wait until the second day to talk about homework. Their first quiz isn’t until day 5 so I’m sure I can wait until day 3 to talk about that. I’m going to embrace the 5-minute maximum that screencast.com has imposed on the world and not talk, for more than 5 minutes at a time, about anything related to course logistics.

### A last note

Just in case you think it is ridiculous that I seem so handcuffed to and by my textbook I want to state my position. If I am using a specific textbook for a course, I like to try to follow its sequencing and notation/conventions as much as possible. If I am going to ask them to try to do some initial learning out of the textbook, I don’t want to make their lives more difficult by making them jump ahead 4 chapters to a place where they vaguely mention ideas that came up in the 4 chapters that we jumped over, and then jump back 3 chapters to cover the stuff that we skipped later. Same thing goes for the notation and conventions: if they are going to see something written in their book umpteen times while trying to make first contact with an idea, I don’t want to further add to their cognitive load by completely switching up the notation and conventions.

### A second last note

This post was supposed to be short. I have no idea what my problem is.

# Resources for selling and running an (inter)active intro physics class

**Posted:**August 10, 2011

**Filed under:**Clickers, Flipped Classroom, Group Quizzes, Introductory Mechanics, SmartPhysics, Student Textbook Reading 9 Comments

This post is in response to Chad Orzel’s recent post about moving toward a more active classroom. He plans to get the students to read the textbook before coming to class, and then minimize lecture in class in favour of “in-class discussion/ problem solving/ questions/ etc.” At the end of the post he puts out a call for resources, which is where this post comes in.

There are three main things I want to discuss in this post, and (other than some links to specific clicker resources) they are all relevant to Chad or anybody else considering moving toward a more active classroom.

- Salesmanship is key. You need to generate buy-in from the students so that they truly believe that the reason you are doing all of this is so that they will learn more.
- When implementing any sort of “learn before class” strategy, you need to step back and decide what you realistically expect them to be able to learn from reading the textbook or watching the multimedia pres

entation. - The easiest first step toward a more (inter)active classroom is the appropriate use of clickers or some reasonable low-tech substitute.

### Salesmanship

I also realized early on in my career that salesmanship is key. I need to explain why I want them to do the reading, and the 3 JiTT (ed. JiTT = Just-in-Time-Teaching) questions, and the homework problems sets, etc. My taking some time periodically to explain why it is all in their best interest (citing the PER studies, or showing them the correlation between homework done and exam grades), seems to help a lot with the end of term evals.

And I completely agree. I changed a lot of little things between my first and second year of teaching intro physics, but the thing that seemed to matter the most is that I managed to generate much more buy-in from the students the second year that I taught. Once they understood and believed that all the “crazy” stuff I was doing was for their benefit and was backed up by research, they followed me down all the different paths that I took them. My student evals, for basically the same course, went up significantly (0.75ish on a 5-point scale) between the first and second years.

A resource that I will point out for helping to generate student buy-in was put together for Peer Instruction (in Computer Science), but much of what is in there is applicable beyond Peer Instruction to the interactive classroom in general. Beth Simon (Lecturer at UCSD and former CWSEI STLF) made two screencasts to show/discuss how she generates student buy-in:

- Introduction to PI for Class: In this screencast Beth runs though he salesmanship slides in the same way that she does for a live class. “You don’t have to trust the monk!”
- Overview of Supporting Slides for Clickers Peer Instruction: In this screencast Beth discusses informally some of the supporting slides which discuss the reasons and value for using Peer Instruction.

### Reading assignments and other “learning before class” assignments

This seems to be a topic that I have posted about many times and for which I have had many conversations. I will briefly summarize my thoughts here, while pointing interested readers to some relevant posts and conversations.

When implementing “read the text before class” or any other type of “learn before class” assignments, you have to establish what exactly you want the students to get out of these assignments. My purpose for these types of assignments is to get them familiar with the terminology and lowest-level concepts, anything beyond that is what I want to work on in class. With that purpose in mind, not every single paragraph or section of a given chapter is relevant for my students to read before coming to class. I refer to this as “textbook overhead” and Mylene discussed this as part of a great post on student preparation for class.

I have tried reading quizzes at the beginning of class and found that it was too hard to pitch them at the exact right level that most of the students that did the reading would get them and that most of the students that didn’t do the reading wouldn’t get them.

Last year I used a modified version of the reading assignment portion of Jitt (this list was originally posted here):

- Assign reading
- Give them 3 questions. These questions are either directly from the JiTT book (I like their estimation questions) or are easy clicker questions pulled from my collection. For the clicker questions I ask them explain their reasoning in addition to simply answering the question.
- Get them to submit via web-form or email
- I respond to everybody’s submissions for each question to try to help clear up any mistakes in their thinking. I use a healthy dose of copy and paste after the first few and can make it through 30ish submissions in just over an hour.
- Give them some sort of credit for each question in which they made an effortful response whether they were correct or incorrect.

I was very happy with how this worked out. I think it really helped that I always responded to each and every one of their answers, even if it was nothing more than “great explanation” for a correct answer. I generated enough buy-in to have an average completion rate of 78% on these assignments over the term in my Mechanics course last time I taught it. I typically weight these assignments at 8-10% of their final grade so they have pretty strong (external) incentive for them to do them.

As I mentioned previously, my current thinking is that I want the initial presentation (reading or screencast) that the students encounter to be one that gets them familiar with terminology and low-level or core concepts. As Mylene says “It’s crazy to expect a single book to be both a reference for the pro and an introduction for the novice.” So that leaves me in a position where I need to generate my own “first-contact” reading materials or screencasts that best suit my needs and this is something that I am going to try out in my 3rd-year Quantum Mechanics course this fall.

It turns out that for intro physics there is an option which will save me this work. I am using smartPhysics this year (disclaimer: the publisher is providing the text and online access completely free to my students for the purposes of evaluation). To explain what smartPhysics is, I will pseudo-quote from something I previously wrote:

For those teaching intro physics that are more interested in screencasting/pre-class multimedia video presentations instead of pre-class reading assignments, you might wish to take a look at SmartPhysics. It’s a package developed by the PER group at UIUC that consists of online homework, online pre-class multimedia presentations and a shorter than usual textbook (read: cheaper than usual) because there are no end-of-chapter questions in the book

~~, and the book’s presentation is geared more toward being a student reference since the multi-media presentations take care of the the “first time encountering a topic” level of exposition.~~My understanding is that they paid great attention to Mayer’s research on minimizing cognitive load during multimedia presentations. I will be using SmartPhysics for my first time this coming fall and will certainly write a post about my experience once I’m up and running.

Since writing that I have realized that the text from the textbook is more or less the transcript of the multimedia presentations so in a way this textbook actually is a reference for the pro and an introduction for the novice. They get into more challenging applications of concepts in their interactive examples which are part of the online homework assignments. For example, they don’t even mention objects landing at a different height than the launch height in the projectile motion portion of the textbook, but have an interactive example to look at this extension of projectile motion.

The thing with smartPhysics is that their checkpoint assignments are basically the same as the pre-class assignments I have been using so it should be a pretty seamless transition for me from that perspective. I still haven’t figured out how easy it is to give students direct feedback on their checkpoint assignment questions in smartPhysics, and remember that I consider that to be an important part of the student buy-in that I have managed to generate in the past.

(*edit: the following discussion regarding reflective writing was added Aug 11*) Another option for getting students to read the text before coming to class is reflective writing, which is promoted in Physics by Calvin Kalman (Concordia). From “Enhancing Students’ Conceptual Understanding by Engaging Science Text with Reflective Writing as a Hermeneutical Circle“, CS Kalman, Science & Education, 2010:

For each section of the textbook that a student reads, they are supposed to first read the extract very carefully trying to zero in on what they don‘t understand, and all points that they would like to be clarified during the class using underlining, highlighting and/or summarizing the textual extract. They are then told to freewrite on the extract. “Write about what it means.” Try and find out exactly what you don‘t know, and try to understand through your writing the material you don‘t know.

This writing itself is not marked since the students are doing the writing for the purposes of their own understanding. But this writing can be marked for being complete.

### Clicker questions and other (inter)active physics classroom resources

Chad doesn’t mention anywhere in his post that he is thinking of using clickers, but I highly recommend using them or a suitable low-tech substitute for promoting an (inter)active class. I use a modified version of Mazur’s Peer Instruction and have blogged about my specific use of clickers in my class in the past. Many folks have implemented vanilla or modified peer instruction with cards and had great success.

**Clicker question resources:** My two favourite resources for intro physics clicker questions are:

- The Ohio State clicker question sequences and,
- The collections put together by the folks at Colorado.

I quite like the questions that Mazur includes in his book but find that they are too challenging for my students without appropriate scaffolding in the form of intermediate clicker questions which can be found in both the resources I list above.

**Clicker-based examples:** Chad expressed frustration that “when I do an example on the board, then ask them to do a similar problem themselves, they doodle aimlessly and say they don’t have any idea what to do.” To deal with this very issue, I have a continuum that I call clicker-based examples and will discuss the two most extreme cases that I use, but you can mash them together to produce anything in between:

- The easier-for-students case is that, when doing an example or derivation, I do most of the work but get THEM to make the important mental jumps. For a typical example, I will identify 2-4 points in the example that would cause them some grief if they tried to do the example completely on their own. When I work this example at the board (or on my tablet) I will work through the example as usual, but when I get to one of the “grief” points I will pose a clicker question. These clicker questions might be things like “which free-body diagram is correct?”, “which of the following terms cancel?” or “which reasoning allowed me to go from step 3 to step 4?”
- The other end of the spectrum is that I give them a harder question and still identify the “grief” points. But I instead get them to do all the work in small groups on whiteboards. I then help them through the question by posing the clicker questions at the appropriate times as they work through the problems. Sometimes I put all the clicker questions up at the beginning so they have an idea of the roadmap of working through the problem.

An excellent resource for questions to use in this way is Randy Knight’s 5 Easy Lessons, which is a supercharged instructor’s guide to his calculus-based intro book. The first time I used a lot of these questions I found that the students often threw their hands up in the air in confusion. So I would wander around the room (36 students) and note the points at which the students were stuck and generate on-the-fly clicker questions. The next year I was able to take advantage of those questions I had generated the previous year and then had all the “grief” points mapped out and the clicker questions prepared for my clicker-based examples.

### Group Quizzes

Not related to clicker questions, but they are related to the (inter)active class: group quizzes are something that I have previously posted about and I have also presented a poster on the topic. I give the students a weekly quiz that they write individually first, and then after they have all been handed in they re-write the quiz in groups. Check out the post that I linked to if you want to learn more about exactly how I implement these as well as the pros and cons. Know that they are my single favourite thing that happens in my class due to it being the most animated I get to see the students being while discussing the application of physics concepts. It is loud and wonderful and I am trying to figure out how to show that there is a quantifiable learning benefit.

# Learning Goals for Calculus-Based Introductory Mechanics using smartPhysics (First Draft)

**Posted:**July 25, 2011

**Filed under:**Introductory Mechanics, Learning Goals, SmartPhysics 9 Comments

I’m on “vacation” right now which means getting some work done in between all the extra time I am spending with my wife and kids while visiting family. My project over the past week was revising and developing new learning goals for my intro mechanics course in the fall.

This year I am using smartPhysics for my first time and there are some topics that I have skipped in the past (such as relative motion) which are quite essential to many other topics (as presented in smartPhysics). So I had to be very thorough in going through the textbook and through the online homework questions to make sure that all the learning goals show up in the most appropriate chapter, that they make sense in the context of the vocabulary used in the textbook, and that ones which were no longer appropriate were removed or suitably revised.

The learning goals in each unit are in roughly the order that they come up. For unit 1, I made them extra fine-grained so that they can easily be checked off as we go instead of at the end of the unit. In Unit 1 we also do the quick and dirty black-box version of derivatives/anti-derivatives so that we can start using them as soon as possible.

Here’s a pdf version if that is more to your liking. Feel free to use any of these learning goals if you like, and feedback is always welcome.

## Learning Goals for Calculus-Based Introductory Mechanics (textbook: smartPhysics)

**Part 1 – Linear Dynamics**

Unit 1 – One-Dimensional Kinematics

- Calculate average velocity during a specified time interval using a position-versus-time graph.
- Calculate or approximate instantaneous velocity at a specific time using the slope of a position-versus-time graph.
- Given a polynomial expression for position as a function of time, use differentiation to find the expression for velocity as a function of time or at a specific time.
- Use graphical integration (area under the curve) to find the displacement as a function of time given a velocity-versus-time curve.
- Given a polynomial expression for velocity as a function of time, use integration to find the expression for the change in displacement as a function of time. Given the displacement at a certain instant in time, find the displacement at some other time.
- Calculate or approximate acceleration at a specific time using the slope of a velocity-versus-time graph.
- Given a polynomial expression for acceleration as a function of time use integration to find the expression for the change in velocity as a function of time. Given the velocity or other necessary information at a certain instant in time, find the velocity at some other time.
- Use graphical integration (area under the curve) to find the velocity as a function of time given an acceleration-versus-time curve.
- Apply the three equations for motion with constant acceleration (i.e, v=v0+at; x=x0+v0t+ at2/2; v2=v02+2a[x-x0]) to solve quantitative kinematics problems in one dimension.
- Compare and contrast the relationship between the direction of the velocity and the acceleration when an object is speeding up, slowing down, or at a turning point.
- Create and interpret motion diagrams. A motion diagram is a pictorial description of an object in motion which shows an object’s position, represented by dots, at equally spaced time intervals. The spacing between dots gives information about the object’s velocity and acceleration. For example, an object that is slowing down is represented by a continuously increasing distance between the dots in the direction that the object is traveling.
- Draw acceleration vectors based on the velocity vectors from a motion diagram, or draw future velocity vectors based on an initial velocity vector and known acceleration vectors.
- Translate between position-versus-time, velocity-versus-time, and acceleration-versus-time graphs. This includes being able to roughly draw the parabolic shape that corresponds to the integration of a linear graph. Calculate or approximate values at a specific time or average values over a specific time range from these graphs.
- Translate between and interpret the different representations of information for the motion of an object in one dimension: word descriptions of motion, kinematic graphs (position, velocity or acceleration-versus-time), motion diagrams, and numerical/symbolic equations/statements.

Unit 2 – Two-Dimensional Kinematics

- Compare and contrast scalars and vectors
- Add and subtract vectors graphically or mathematically by breaking the vectors into Cartesian components.
- Convert between the two major two-dimensional vector representations: Cartesian components (using x and y components along with unit vectors) and polar coordinates (magnitude and angle).
- Describe the horizontal and vertical components of velocity and acceleration at every point along the trajectory for an object undergoing projectile motion.
- Solve projectile motion problems for objects whose motion starts and ends at the same height (such as kicking a ball in a soccer field) or at different heights (such as throwing an object onto a roof or off of a bridge).
- Discuss the assumptions required to be able to correctly apply the range equation. Recognize the two following insights provided by the range equation: maximum range occurs for a launch angle of 45 degrees, and the range for complimentary angles is the same.
- Demonstrate mastery of “Unit 1 – One-Dimensional Kinematics” learning goals in two or three-dimensional situations.
- Apply the three equations for motion with constant acceleration to solve quantitative kinematics problems in two or three dimensions.

Unit 3 – Relative and Circular Motion

- Translate displacement and velocity between two different frames of reference.
- There are no specific learning goals for these sections.
- Relate an object’s velocity or angular velocity to its period of rotation which is the time it takes the object to make one revolution.
- Perform calculations relating an object’s centripetal acceleration; its instantaneous velocity or angular velocity; and the radius of curvature of its path.
- Explain how an object can have a non-zero acceleration even if its speed is constant.
- Compare and contrast the direction of acceleration for objects undergoing constant speed circular motion and varying speed circular motion.

Unit 4 – Newton’s Laws

- Recognize what does and does not constitute a force. Identify the specific forces acting on an object.
- Use superposition to find the net force acting on an object.
- Qualitatively relate the net force acting on an object to its motion.
- Perform calculations using Newton’s Second Law which relates the net force on an object, the object’s mass and its acceleration.
- There are no specific learning goals for this section. Learning goals for the concept of momentum are found in the Unit 12 learning goals.
- There are no specific learning goals for this section.
- Discuss why a given reference frame is or isn’t an inertial reference frame.
- Identify the action-reaction force pairs produced by two interacting bodies.
- Recognize situations where two or more objects have the same acceleration due to maintaining contact with each other or being attached to each other. Solve problems involving these situations including finding the net force acting on each of these objects.

Unit 5 – Forces and Free-Body Diagrams

- Compare and contrast the concepts of mass and weight.
- Correctly identify the normal force (magnitude and direction) exerted on an object by a surface with which it is in contact. Correctly identify the tension force (magnitude and direction) exerted on an object by a string, rope or other similar object with which it is in contact.
- Relate the restoring force applied by a spring to the distance which has been stretched or compressed relative to its relaxed position and the stiffness of the spring.
- Solve problems using the Universal Law of Gravitation which relates the attractive gravitational forces two objects exert on each other to their masses, the distance between them, and the universal gravitation constant.
- Draw an accurate free-body diagram of a system, which includes excluding forces which are internal to the system (such as 3rd law force pairs).
- Calculate the apparent weight of an object and relate the motion of an object to descriptions/graphs of its apparent weight. Apparent weight is the support force which would be measured by an object such as a bathroom scale (which measures the normal force applied to the object) or a rope attached to a force scale (which measures the tension force holding up the object).
- Calculate the magnitude of the gravitational force and the normal force (apparent weight) acting on a body at rest or moving in one dimension.
- Translate between expressions/graphs of net force acting on an object as a function of time and the resulting expressions/graphs for position or velocity as a function of time.

Unit 6 – Friction

- Calculate the static or kinetic friction forces acting on a body. This includes determining if it is a static of kinetic friction force that is present in a given situation.
- Given both static and kinetic friction coefficients, determine if an object is at rest or in motion relative to a surface with which it is in contact for situations such as a block on a ramp, attempting to slide an object across a surface or attempting to pull a surface out from under an object.
- Correctly identify the direction of the net force required to keep an object travelling in a circle at a constant speed.
- Solve “rounding a curve” problems that involve friction, a banked curve or both. These problems may involve finding quantities such as the radius of the curve, the speed of the object, a coefficient of friction or the angle of the bank.

**Part 2 – Conservation Laws**

Unit 7 – Work and Kinetic Energy

- Calculate the work done by a constant force on a body that undergoes a displacement.
- Calculate the kinetic energy of an object.
- Perform calculations using the work-kinetic energy theorem, which relates the net work done on an object to its change in kinetic energy.
- Find the dot product of two vectors using vector components, or using the magnitude of the vectors and the angle between. Use the result of a dot product to find an unknown vector component or the angle between two vectors.
- Identify if the net work done on an object is positive, negative or zero based on the relative directions of the net force being applied and the body’s displacement. Relate the motion of an object (speeding up or slowing down) to the sign of the net work (positive or negative) which has been done to it.
- Calculate the net work done when many forces are applied to an object.
- Recognize the work-kinetic energy theorem as a statement of the conservation of energy.
- Calculate the work done on an object by a varying force, a technique which requires the use of integration.
- Relate the work done by a spring to the initial and final distances it has been displaced (stretched or compressed) from its relaxed position.
- Recognize that the work-kinetic energy theorem is valid for varying forces and displacements along a curved path, in addition to constant forces applied along straight paths.
- Recognize that work done by a conservative force depends only on the endpoints (initial and final positions) and not on the specific path traveled between those endpoints.

Unit 8 – Conservative Forces and Potential Energy

- Recognize that the work done by a conservative force around a closed path is zero.
- There are no new learning goals for this section.
- Recognize the distinction between conservative and nonconservative forces.
- Recognize that mechanical energy is conserved whenever the net work done by all non-conservative forces is zero.
- Calculate the change in gravitational potential energy in a system.
- Explain how two different people could get two different values for the gravitational potential energy of a system.
- Use conservation of mechanical energy to analyze mechanics problems involving kinetic and gravitational potential energies.
- Calculate the change in elastic potential energy in a system due to the compression or extension of a spring, or due to the work done on or by a spring.
- Use conservation of mechanical energy to analyze mechanics problems involving kinetic, gravitational potential energies and elastic potential energies.
- Solve problems in which both conservative and nonconservative forces act on a moving body.

Unit 9 – Work and Potential Energy

- Perform calculations involving the work done by a nonconservative force such as friction.
- We will be covering only the sections “9.2 – Box Sliding Down a Ramp” and “9.3 – Work Done by Kinetic Friction.”

Unit 10 – Center of Mass

- Locate the center-of-mass of a two-body system, of a multi-body system, for continuous mass distributions, or for a system of objects. For continuous mass distributions, the most challenging integral you will be asked to perform is the integration of a polynomial expression.
- Analyze systems consisting of multiple bodies and/or continuous mass distributions using the center-of-mass versions of the work-kinetic energy theorem (called the center-of-mass equation) or Newton’s Second Law (called the equation of motion for the center of mass).
- Convert between the lab and center-of-mass reference frames

Unit 11 – Conservation of Momentum

- Calculate the momentum of an object.
- Recognize that the total momentum of a system is conserved (is constant) when the total external force applied to this system is zero.
- Analyze inelastic collisions using conservation of momentum. Note that the term collisions also includes “collisions in reverse” such as explosions and recoil.
- Recognize that kinetic energy is not conserved in inelastic collisions, and that this is a consequence of the internal forces being non-conservative. Discuss the forms of energy to which this lost kinetic energy is converted.
- Analyze inelastic collisions in the center-of-mass reference frame and recognize that the total momentum is always zero in this reference frame.

Unit 12 – Elastic Collisions

- Recognize that kinetic energy is conserved in elastic collisions, and that this is a consequence of the internal forces being conservative
- Analyze elastic collision collisions in the lab frame and the center-of-mass reference frame.

**Part 3 – Rotational Dynamics**

Unit 14 – Rotational Kinematics and Moment of Inertia

- Describe the rotation of a rigid body in terms of angular position, angular velocity, and angular acceleration.
- Analyze rigid-body rotation when the angular acceleration is constant using the rotational equations of motion.
- Translate between the linear parameters of distance, speed and acceleration to the rotational parameters of angle (angular distance), angular velocity and angular acceleration at a point on a rotating rigid body.
- Use superposition to determine the moment of inertia of a system for a number of point-like or solid objects. Although we will discuss how to find the moment of inertia of solid objects such as cylinders and spheres, you will not be asked to find the moment of inertia of these objects on your own.
- Determine the moment of inertia of a rod or other one-dimensional solid object where the calculation requires the integration of a polynomial.
- Determine the rotational kinetic energy of a system of objects of known moments of inertia about a given axis of rotation.

Unit 15 – Parallel Axis Theorem and Torque

- Find the cross product of two vectors using vector components, or using the magnitude of the vectors and the angle between. Use the result of a cross product to find an unknown vector component or the angle between two vectors.
- Determine the net torque about a certain point due to one or more forces.
- Use the rotational analog of Newton’s second law (the net torque is equal to the product of the moment of inertia and the angular acceleration) to analyze a rotating rigid body.
- We will be covering only the sections “15.4 – Torque and Angular Acceleration”, “15.5 – Example: Closing a Door” and “15.6 – Torque and the Cross Product.”

Unit 16 – Rotational Dynamics

- Calculate work in a rotational system which is the integral of the net torque over the angular displacement.
- Find the total kinetic energy of a solid object which is sum of the kinetic energy of its center of mass and its rotational kinetic energy, which is due to the rotation of the object around an axis through its center of mass.
- Analyze systems consisting of both translational and rotational motion (such as a rolling ball) using dynamics and/or energy.

Unit 17 – Rotational Statics: Part 1

- Find the torque due to the weight of an object by treating it as if the entire mass of the object is located at its center of mass.
- For a system in equilibrium, find all the forces acting on the system. Some forces may need to be resolved into normal and frictional forces.

Unit 19 – Angular Momentum

- Relate the angular momentum of a system to its moment of inertia and angular velocity.
- Analyze collisions or deformation in rotating systems using conservations of momentum. Examples of collisions include a person stepping onto or off of a merry-go-round. An example of a deformation is a person on a merry-go-round making their way toward the center.

**Course-Scale Learning Goals**

- Be fluent with your physics vocabulary. Be able to compare and contrast, or distinguish between terms which are often used interchangeably outside of physics such as speed and velocity, or between terms which sound similar, but are completely different such as potential and potential energy.
- Use proportional reasoning. For example be able to correctly determine that an object travelling at a speed 2v has a kinetic energy (K=mv2/2) that is 4 times that of when it was travelling at a speed of v.
- List the assumptions made for a given model and be prepared to discuss the weaknesses of each assumption.
- Perform unit conversions.
- Verify that an equation is dimensionally consistent, that is by using the appropriate unit conversions, you can verify that both sides of an equation have the same units.
- Explain and follow the rules for keeping track of significant figures in your calculation.
- Make use of graphical interpretation for situations where differentiation and integration would normally be used. Examples include finding the slope of a velocity-versus-time graph to find acceleration or integrating a force-versus-displacement graph to find work.
- Derive appropriate physical parameters of a system when presented with a graph. Examples include using the slope of a velocity-versus-time graph to find acceleration or finding the area under the curve (graphical integration) for a force-versus-displacement graph to find work.
- Transfer the techniques and concepts learned in this course to novel contexts (that is being able to solve problems which do not map directly to those which have been previously encountered).

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