### Notes:

The Case Studies: Circular Motion Concept Builder is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Concept Builder can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

### Teaching Ideas and Suggestions:

Many Physics courses include a unit on Circular Motion or include the topic in a unit on Newton's Laws. It is a common practice in most physics courses to discuss the mathematics of moving in circles. This includes the presenation of equations and a demonstration of their use in the analysis of physical situations. More often thatn not the analysis involves using the formulas in a plug-and-chug fashion. Numerical values are given for all but one of the quanities in the forrmula and it becomes the burden of the student to solve for the unknown quantity. Such a practice has plenty of merit and we have devoted an entire section of our website to support students (and teachers) who are devoted to such a practice. See the Calculator Pad.

This Concept Builder takes a different approach to the use of mathematical formulas associaed with circular motion. In this Concept Builder, students use the formulas as a guide to thinking about how a change in one variable affects the other variables. So rather than using the formulas as an algebraic recipe for solving a problem for an unknown value, they use the formulas to think proportionally about how (for instance) differences in speed might affect the acceleration of two objects.

Each question involves two objects or cases. Information about the two objects are presented to students. For instance, the question might tell the student that the object in Case A has twice the mass and three times the speed as the object in Case B. The student must then use the formula for net force to identify how many times greater the net force is for Case A compared to Case B. Such a question demands that students understand the equation as a proportionality. Answering such a question does not involve algebraic manipulation and substitution into a formula.

This Concept Builder was intended as an in-class activity. We recommend its use in the later stages of the unit after the topic has been presented, discussed, "labbed", and applied. The Concept Builder includes three activities. Teachers using the Concept Builder with their classes should preview the Concept Builder (or view the Questions in the separate file) in order to judge which activities would be most appropriate for their students. Our summary of the three activities is as follows:

• Activity 1: Speed Question Groups 1-4 Effect of Radius and Period on Speed
• Activity 2: Acceleration Question Groups 5-8 Effect of Speed and Radius on Acceleration
• Activity 3: Net Force Question Groups 9-12 Effect of Mass, Speed, and Radius on Net Force

In order to complete an activity, a student must correctly analyze each question for that activity. If a student's analysis is incorrect, then the student will have to correctly analyze the same or very similar question twice in order to successfully complete the activity. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through an activity, a system of stars and other indicators are used to indicate progress on the activity. A star is an indicator of correctly analyzing the question. Once a star is earned, that question is removed from the que of questions to be analyzed. Each situation is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the question and will have to correctly analyze it twice before earning a star. A yellow box is an indicator that the question must be correctly analyzed one time in order to earn a star. Once every question in an activity has been analyzed, the student earns a medal which is displayed on the Main Menu. This system of stars and medals allows a teacher to easily check-off student progress or offer credit for completing assigned activities.

The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each question group is accompanied by a Help page that discusses the specifics of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the section titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.

### Related Resources

There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Case Studies: Circular Motion Concept Builder. These include:

• Minds On Physics Internet Modules:
The Minds On Physics Internet Modules include a collection of interactive questioning modules that help learners assess their understanding of physics concepts and solidify those understandings by answering questions that require higher-order thinking. Assignments CG1 through CG5 of the Circular Motion and Gravitation module provide great complements to this Concept Builder. They are best used in the middle to later stages of the learning cycle. Visit the Minds On Physics Internet Modules.

Users may find that the App version of Minds On Physics works best on their devices. The App Version can be found at the Minds On Physics the App section of our website. The Circular Motion and Gravitation module can be found on Part 2 of the six-part App series. Visit Minds On Physics the App.

• Physics Interactives: Our Physics Interactives section include an interactive simulation that makes for a perfect pre-cursor to this Concept Builder. It is called Uniform Circular Motion. When combined with the accompanying activity sheet, it makes for an excellent activity to help students understand the dependence of the variables on one another for objects moving in circles.

Visit Uniform Circular Motion

Additional resources and ideas for incorporating Case Studies: Circular Motion into an instructional unit on circular motion can be found at the Teacher Toolkits section of The Physics Classroom website.  Visit Teacher Toolkits.