# Introduction to Angular Motion

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## Objective

Students will be able to qualitatively and quantitatively define angular displacement, velocity, and acceleration.

#### Big Idea

Students roll into a unit on circular motion as they define theta, omega, and alpha (oh my)!

## Context

This is the first lesson in our rotational motion unit, so students are working with a clean slate today. They already have a strong background knowledge of linear motion concepts, such as velocity and acceleration. My goal today is to introduce the concept of angular displacement, speed and acceleration, so class starts with a short inquiry activity (SP2). Then, students define each angular quantity (in preparation to address HS-PS2-4) before class ends with collaborative problem solving (SP5).

The only material required for this lesson is a class set of protractors.

## Angular Displacement Inquiry Activity

15 minutes

Class starts with an inquiry activity that asks students to use a protractor to measure the range of motion of their knees. I have the activity displayed on the front board as students enter the room, and they are also able to grab a protractor on their way to sitting down. The displayed question and the protractor are the only materials students need to get started, but to bring an official start to class I read the question aloud.

Students work in pairs for this activity, although they can choose to work individually if they prefer. The goal is to get students thinking about how to measure something that is rotating. To date, our AP Physics 1 course has focused on linear motion and I want to force students out of their comfort zones by asking them to measure something that can rotate. I purposely haven't given a procedure for this activity, since I'm also using it as a method to assess how much prior knowledge students have about angular displacement.

As students are discussing the questions and measuring ranges of motion, I walk around to informally observe methods of measurement and students' conversations. As I'm circulating students might ask for guidance on how to measure their ranges of motion, but I try to stay passive because I want this to be a true inquiry activity. I'm not looking for a specific answer; instead I want students to reacquaint themselves with protractors and measuring angles.

After about ten minutes, I collect the protractors and ask students to verbally share their responses. The response sharing is quite informal, as different students raise their hands and everyone who wants to share is given that opportunity. Some students might comment on what others share, and I might ask for clarification on some statements. The purpose of our discussion is to get students thinking about angles, but I'm also assessing the students' prior knowledge with what information they share. While my students have an excellent math background and know a lot about angles, if they struggle with this activity then I offer a supplementary on-line review packet or before-school review session. When there are no more students wishing to share, we move into the next part of the lesson, which defines angular displacement (and angular velocity and acceleration).

## Introducing Angular Motion

20 minutes

It's time for students to take out their notebooks to copy down equations and definitions of angular displacement, velocity, and acceleration. My students are operating under the expectation that they must write down key points from the presentation. This expectation of how to take notes has been outlined and ingrained in their learning since freshman year. Because these are AP students, how they organize their notes (notebook, binder, etc.) is a decision the individual student gets to make. I assume at this point in their high school careers they have an established system to stay organized.

I display the angular speed & acceleration notes (also available as a PowerPoint) to help the students understand what they need to write down. I have a hard copy of the slides in my hands as I circulate throughout the room, which includes notes (viewable when the PPT file is downloaded). These notes help me to stay focused and ensure I mention the highlights as we progress through each slide. I usually have a lot of interaction with my students throughout the presentation. The students ask questions, participate in solving any examples, and connect to real-world situations to stay engaged the entire time.

The specific goal of these notes is to define angular position, angular velocity, and angular acceleration. Also, while students are often familiar with radians, degrees, and revolutions, they have often forgotten the conversion factors, so we spend some time discussing that as well. The notes start by defining each quantity with equations and pictures. Then, the students can apply these definitions as we work through several examples. Before I provide the solution to each example, I give students several minutes to read and think about the problem (individually or with those seated near them). Then, I ask students to contribute information as I walk them through the solution.

## Collaborative Problem Solving for Angular Motion

15 minutes

As closure and an informal summative assessment, students have the rest of the class to start tonight's homework from our textbook. The assessment is summative as it includes use of linear motion concepts that were learned earlier in the school year. I call it informal because I don't want students to get nervous that it will count as a quiz or test grade. Since my goal is to assess their level of understanding and use of prior knowledge, I will collect and grade the assignment for accuracy at the start of the next class meeting. Not only do I want to give students personalized feedback on this homework assignment, I also want to check the pacing of the course and make sure my students are ready to move on to the next lesson.

Students can move to sit near peers that they'd like to work with on today's homework. This is an assignment that needs to be completed by each student on a separate sheet of paper, although they may use those seated around them as a resource while working in class, as I encourage collaboration. The problems that I choose are specifically asking students to calculate arc length, angular displacement, angular velocity, and angular acceleration. While most of the questions are straight forward since these are brand new concepts for the students, some do require students to convert between revolutions, degrees, and radians.

This is our closure activity for today and it's meant to have students apply their newly learned knowledge from the paired reading activity. I am also trying to take a step towards a flipped classroom. I like students to have me as a resource when they work through problems, and I think it helps them build confidence. In the past I've attempted to do entire class periods of a full flipped classroom, but it's hard to hold the students accountable for digesting the needed material. I find that a combination of work time (that lasts right up until the bell rings) and in-class learning best fits the needs of my students.