**AP/Calculus-Based Physics:** Kinematics: The Physics of Motion Units

This topic contains a selection of units designed to assist you in teaching motion. Units include frames of reference, graphing skills, motion in one dimension, motion in more than one dimension, vectors, and more. Units are not listed in a prescribed order.

### Graphing (12)

#### Lesson Plans:

This is a PhET Gold Star winning lesson that helps students build skills in interpreting graphs of motion. It accompanies the PhET simulation "The Moving Man" (see link below) and includes classroom-ready Power Point concept questions, student guide, and assessments. *Note:** This lesson is appropriate for more advanced students than the lesson listed directly above. You must be a registered user to access it, but registration is free.*

**Item Type:**Teaching Module

**Level:**Grades 10-12

**Duration:**2 Class Periods

High school students can often record data and "plug & chug", but have more difficulty in fitting or interpreting data. This exemplary two-week unit on data analysis introduces students to the statistical method known as least squares regression. Using an online tool to plot data, students then calculate regression lines and fit the data to estimated parameters.

**Item Type:**Instructional Unit

**Level:**Grades 9-12

**Duration:**Two Weeks

#### Activities:

This website contains a collection of short videos depicting physical processes commonly discussed in beginning courses. Positions of objects in the video frame can be viewed in step motion or real-time, and then mapped onto video analysis software, allowing for more accurate measurement and graphing.

**Item Type:**Video Collection

**Level:**Grades 9-12

This set of eleven interactive challenges will help students master motion graphing. Each challenge requires the student to match the motion of an animated car to the correct position/time or velocity/time graph. The activity provides enough repetition to help learners construct a meaningful understanding of why the graphs appear as they do.

**Item Type:**Interactive Problem Set

**Level:**Grades 9-12

**Duration:**30-40 minutes

Maneuver a simulated man and watch simultaneous graphs of his position, velocity, and acceleration. For beginning learners, the acceleration graph may be closed. Try teaming this simulation with the great companion lessons by PhET teacher-fellows, found under "Lesson Plans" above. *Highly versatile resource; adaptable to a broad spectrum of abilities/levels.*

**Item Type:**Interactive Simulation

**Level:**Grades 6-12

**Duration:**One Class Period

#### References and Collections:

This robust browser-based tool lets users perform calculations, share designs, and create interactive Whiteboard resources. Choose from Cartesian or polar grids, select angle measurement in degrees or radians, and view parabolic graphs in standard, vertex, or intercept form. You can zoom in/out, drag a graph onto the page, and change axes. The platform also supports conic sections, Fourier expansions, and polar graphing. When you finish, you can publish your resource or embed the file into a virtual learning space.

**Item Type:**Technology Tool

**Level:**Grades 6-12

#### Content Support For Teachers:

A very well-organized tutorial on how to construct and interpret three basic kinematic graphs: P/T, V/T and A/T. It includes animated examples, links to five worksheets, and related problems for student exploration.

**Item Type:**Online Tutorial

**Level:**Grades 8-12

**Duration:**One Class Period

#### Student Tutorials:

This is a web-based homework problem that helps students understand velocity vs. time graphs (v vs. t). A sequence of user-activated questions guides beginners through a full conceptual analysis before introducing the math. Based on principles of physics education research (PER).

**Item Type:**Interactive Problem

**Level:**High School Physics

**Duration:**30 minutes

Excellent self-guided tutorial promotes understanding of "position" as a physics concept. Contains multiple graphs, animations, and interactive opportunities for students to test their comprehension.

**Item Type:**Interactive Tutorial

**Level:**Grades 8-12

**Duration:**One Class Period

A companion to the resource above, this online tutorial explores the importance of the slope of v-t graphs as a representation of an object's acceleration. Self-guided evaluations help students overcome common misconceptions.

**Item Type:**Interactive Tutorial

**Level:**High School Physics

**Duration:**45 minutes

#### Assessment:

A set of homework problems (with answers) written by the PhET team to accompany "The Moving Man" simulation. It assesses student understanding of graphs of position, velocity, and acceleration. *Note:** You must be a registered user of PhET to access this resource. Registration is easy and free.*

**Item Type:**Problem Set

**Level:**High School

**Duration:**One Class Period

Here is a set of free assessment tools for grades 6-12 on topics related to physics and biology. Within the sub-topic of Force and Motion, you'll find assessments to gauge understanding of kinematics, the relationship of motion and force, and momentum. Diagnoser assessments are aligned with the NGSS, and include elicitation (warm-ups) and developmental lessons. After completing the lesson, students answer digital question sets on specific topics, with immediate feedback provided to both teachers and learners. The final step in the process is "Prescriptive Activities", designed to target specific problematic areas located by Diagnoser.

**Item Type:**Assessment Tool

**Level:**Grades 6-12

### Vectors (8)

#### Lesson Plans:

A unique and highly engaging two-week unit on vectors. Beginning physics students build understanding of vector properties by doing real pilot navigation training. This problem-based learning module comes with complete guides for teacher and learner. The final assessment is a virtual pilot test flight. *Cost-free with teacher registration*

**Item Type:**Instructional Unit

**Level:**High School

**Duration:**Two Weeks

This is an exemplary set of tutorial materials for teachers to introduce vector basics, including vector addition/subtraction and how to calculate vector components. See Assessments below for a companion unit test. All may be freely downloaded. To read about the underlying pedagogy employed by the authors, go to Reference Material below and click on *Bridging the Vector Calculus Gap*.

**Item Type:**Power Point Presentation

**Level:**High School Physics

**Duration:**1-2 Class Periods

#### Activities:

This animation gives students a highly visual way to see how the math works in vector addition. You can input 2-5 forces, then the animation shows the parallel translations of the force arrows and auto-generates the resultant. Available in HTML5 or Java. *Great resource for students who are struggling with the content.*

**Item Type:**Interactive Animation

**Level:**High School Physics

**Duration:**30 minutes

Any vector directed in two dimensions can be thought of as having two parts (components). In this interactive, students input the magnitude of force and enter values for degrees of the first and second angle, then click "Find Out Components". The resource animates the resolution process, displays magnitudes of the components. Available in HTML5 or Java.

**Item Type:**Interactive Animation

**Level:**High School Physics

**Duration:**30-40 minutes

#### Student Tutorials:

This page is an interactive environment where subjects are organized in flow charts, allowing easy movement from one topic to a related item. Vector resolution, addition, and product are covered in-depth.

**Item Type:**Online Tutorial

**Level:**Grades 9-12

**Duration:**30 minutes

As instructors, we may forget that certain representations (like vector arrows) seem like a foreign language to beginning students. This thoughtfully-crafted tutorial introduces vector diagrams in kid-friendly language and extends the learning to interactive practice problems with answers provided.

**Item Type:**Digital Tutorial

**Level:**Grades 8-12

**Duration:**One Class Period

#### Assessment:

This online interactive problem was developed by a physics professor to give students guided practice in subtracting vectors. Immediate feedback is given for both correct and incorrect responses.

**Item Type:**Interactive Problem

**Level:**High School Physics

**Duration:**20 minutes

This comprehensive worksheet on vectors may be used as a test/quiz for beginning physics students. It was designed to accompany the lecture and lesson materials by the same authors (see above under Lesson Plans). May be freely downloaded and printed for classroom use.

**Item Type:**Assessment/Test

**Level:**High School Physics

**Duration:**One Class Period

### Motion in One Dimension (7)

#### Activities:

A simulation to explore the motion of a model car with constant acceleration. The student sets values for initial position, velocity and acceleration -- the simulation creates the real-time graphs. A pair of timers can be placed anywhere along the path of the car to measure the motion at intervals. Available in HTML5 or Java. *Can be adapted for grades 6-7 by using only the velocity and position fields.*

**Item Type:**Interactive Simulation

**Level:**Grades 6-12

**Duration:**30 minutes

This PBL activity was developed to promote understanding of the universal law of gravitation. Students work cooperatively on a mock space mission: a spacecraft is orbiting Iris, a planet with a smaller radius and lower mass than Earth. Students collaborate to find the gravitational acceleration on the surface of Iris and figure out how a human body will react to gravity on the planet. *Student Guide is freely accessible; answer key is available by contacting the author.*

**Item Type:**Problem-Based Learning

**Level:**Grades 11-12

**Duration:**One Class Period

How does air resistance affect the motion of a free-falling object? In this model, a blue ball falls under the influence of gravity alone. The red ball is subject to both gravity and air resistance. Adjust the amount of air resistance with a slider, then watch the changes in the motion graphs. **Requires Java**

**Item Type:**Interactive Simulation

**Level:**Grades 9-12

**Duration:**30 minutes

#### Content Support For Teachers:

This item, part of an online textbook, offers in-depth content support for teachers, plus sets of problems related to speed and velocity. It includes creative ideas for classroom investigations that integrate statistics.

**Item Type:**Reference Material

**Level:**Teacher Support

This resource offers support in understanding the concept of acceleration as a rate of change. It includes example problems with solutions, homework problems, and a fun section that provides sample accelerations of selected events. Great content support for middle school teachers or solid tutorial for high school physics.

**Item Type:**Online Tutorial

**Level:**Tchr Support & HS Physics

This page offers a clear explanation of the equations that can be used to describe the motion of an object in a straight line. A comprehensive set of algebraic, statistical, and conceptual problems are included. Provides content support for middle school teachers.....also appropriate for high school physics students.

**Item Type:**Online Tutorial

**Level:**Grades 9-12

#### Student Tutorials:

This is a web-based homework problem that helps students understand velocity vs. time graphs (v vs. t). A sequence of user-activated questions guides beginners through a full conceptual analysis before introducing the math. Based on PER principles (physics education research).

**Item Type:**Interactive Problem

**Level:**High School Physics

**Duration:**30 minutes

### Motion in More Than One Dimension (11)

#### Lesson Plans:

Students learn about projectile motion and conservation of momentum as they investigate a mock-murder case involving a handgun. They are given just enough data about the gun ballistics and the crime scene to test hypotheses and solve the murder. This resource is based on the PBL (Problem-Based Learning) instructional method. *The Student Guide is freely accessible; an answer key can be obtained by contacting the author.*

**Item Type:**Problem-Based Learning

**Level:**High School Physics

**Duration:**Two Class Periods

#### Activities:

Students can have fun exploring projectile motion as they interactively fire objects of varying mass from a cannon. Users may set initial velocity, angle, and air resistance. This resource would be teamed well with the Physics Classroom student tutorial on projectile motion (below).

**Item Type:**Interactive Simulation

**Level:**Grades 6-12

**Duration:**One Class Period

This simulation would be a good follow-up to the PhET projectile motion applet (above). This item takes the learner to the next level by calculating maximum height, horizontal distance, magnitude of velocity, and total energy of a projected object. Students will set initial height, speed, angle, and mass before firing their projectile. *Appropriate for high school or gifted/talented middle school students.*

**Item Type:**Interactive Simulation

**Level:**Grades 8-12

**Duration:**45 minutes

A great activity for getting students excited about projectile motion.....and easily adaptable for the high school classroom. It is a CSI scenario where a man is shot with a handgun. Using the Problem-Based Learning method, students work cooperatively to solve the case by applying physics. This resource includes a printable student manual. Registered teacher-users can also access an Instructor's Guide free of cost.

**Item Type:**Problem-Based Learning

**Level:**High School Physics

**Duration:**Two Class Periods

19 videotaped experiments are organized sequentially here for introducing fundamentals of motion in introductory physics classes. The instructional method is based on cognitive apprenticeship: students focus on the * process* of science by observing, finding patterns, modeling, testing, and revising. The author is a highly-respected professor of physics, who has done extensive work in physics education research.

This simulation features an airplane flying at constant horizontal velocity, preparing to drop relief supplies to a small island. As captain of the plain, you must calculate the release point for dropping the package and press the red release button at the right moment. The trajectory of the falling package is traced onscreen. If your calculations were off, it will dump in the ocean. *Question for students to ponder: what does inertia have to do with it?*

**Item Type:**Interactive Simulation

**Level:**Grades 9-12

**Duration:**20-30 minutes

This popular sim has been converted to HTML5 and dressed up with cool new features. As with the older version, students will set initial speed & angle, and choose from a variety of projectiles (pumpkin, piano, cannonball, person). Now they can also set drag coefficient and easily see how air resistance affects the trajectory. You can also adjust the gravitational constant and manually adjust the diameter of the projectile. *Very robust, very easy to adapt to different learning levels!*

**Item Type:**Interactive Simulation

**Level:**6-12

**Duration:**One Class Period

#### Content Support For Teachers:

This easy-to-follow tutorial helps students comprehend how various components work together to determine trajectory: range, height, time, speed, and angle. It includes explanations of algebra-based equations related to projectile motion.

**Item Type:**Reference Material

**Level:**Teacher Support

#### Student Tutorials:

This seven-part resource is an excellent introduction to the characteristics of projectile motion. Through in-depth explanations and animations, it explores vertical acceleration and explains why there are no horizontal forces acting upon projectiles, a common student misconception. The last two sections are devoted to problem solving. Try teaming it with the PhET Projectile Motion activity above.

**Item Type:**Interactive Tutorial

**Level:**Grades 8-12

**Duration:**45 minutes

A unique and highly-engaging tutorial developed by the authors of Australia's *PhysClips*. Short film clips, photos, and diagrams are integrated with simple text to spark interest. The first two videos feature the classic "Hammer and Feather Drop", both on the moon and on Earth.....a great springboard to discuss air resistance.

**Item Type:**Multimedia Tutorial

**Level:**High School

**Duration:**1-2 Class Periods

#### Assessment:

This interactive problem goes well beyond the formulas to help learners separately analyze both the horizontal and vertical components of motion in a ball-throwing scenario......__before__ they attempt any math. Great scaffolding is provided from conceptual reasoning through calculation, with immediate feedback for correct and incorrect responses. It also addresses both Math and Language Arts Common Core standards.

**Item Type:**Interactive Tutorial

**Level:**High School Physics

**Duration:**20 minutes

### Circular Motion (8)

#### Activities:

This set of activities developed by the Exploratorium offers students an entertaining way to see real-world applications of rotational dynamics and principles of circular motion. They will explore forces at work in "The Ollie" and torque forces required for mid-air maneuvers. **Note:** Running the accompanying videos requires Flash.

**Item Type:**Classroom Activity Set

**Level:**Grades 9-12

**Duration:**One Class Period

For the teacher planning a unit on amusement park physics, this tutorial can double as a student classroom activity. It offers an overview of the forces acting upon a roller coaster as it travels on a straight, curved, or looped track. Free body diagrams and animations depicting kinetic/potential energy also enhance student understanding of a complex set of interactions. (Includes a self-test.)

**Item Type:**Interactive Tutorial

**Level:**Grades 8-12

**Duration:**One Class Period

This is Part 2 of the mock mission to Planet Iris * (see Part 1 under the heading "Motion in One Dimension" above)*. In this scenario, students work in groups to determine the velocity required to maintain a stable orbit at 140m above the surface of Iris. then calculate the thrust necessary to land the spacecraft smoothly. Includes a printable student manual. Registered teacher-users also have access to a comprehensive instructor's guide.

**Item Type:**Problem-Based Learning

**Level:**High School Physics

**Duration:**2 Class Periods

Students will have fun as they design a flat circular highway exit and figure out what the exit speed limit should be. They will be applying concepts of circular motion, static friction, and kinetic friction. For the AP classroom, the activity can be extended to the design of a banked curve. A complete instructor's guide is available free of cost to registered teacher-users.

**Item Type:**Problem-Based Learning

**Level:**High School Physics

**Duration:**2-3 Class Periods

This interactive simulation offers a way for students to explore the connection between uniform circular motion and simple harmonic motion. It provides a way to visualize SHM as the projection of uniform circular motion onto one axis, which should promote understanding of the basic equation for objects undergoing simple harmonic motion.

**Item Type:**Interactive Model

**Level:**High School Physics

**Duration:**One Class Period

#### Content Support For Teachers:

One of the most deeply entrenched misconceptions among beginning physics students is that centrifugal motion (away from the center) is a "force" in itself. In this tutorial, part of *Physics Classroom*, the author explains why the direction of force is viewed from an inertial frame of reference in a classical mechanics course and thus why centrifugal motion is not a force in a Newtonian framework.

**Item Type:**Interactive Tutorial

**Level:**Grades 8-12

#### Student Tutorials:

This resource guides the beginning student through characteristics of circular motion. It is broken into five sections addressing: the mechanics of circular motion, centripetal force, algebraic and trigonometric problems and solutions, and a full chapter that debunks the centrifugal "force" misconception. Interactive problems feature liberal use of diagrams and force vectors to enhance understanding.

**Item Type:**Interactive Tutorial

**Level:**High School

**Duration:**60-90 minutes

This student tutorial illustrates how circular motion principles can be combined with Newton's Second Law to analyze physical situations. Two algebraic problems and detailed solutions are provided, plus a five-step model for solving circular motion problems.

**Item Type:**Interactive Tutorial

**Level:**Grades 9-12

**Duration:**45 minutes

### Planetary Motion (3)

#### Activities:

Explore Kepler's Laws in this simulation that allows students to control the size and path of an object orbiting one of the planets in our Solar System. You can modify the eccentricity and adjust the axial radius. The simulation generates radial lines, graphs of Period vs. Semimajor Axis and more. Don't miss the "About" link to supporting resources: student manuals, assessment materials, and more. *Note** This resource requires Flash*

**Item Type:**Interactive Simulation

**Level:**High School

**Duration:**30-45 minutes

With this orbit simulator, you can set initial positions, velocities, and masses of 2, 3, or 4 bodies, and then watch them orbit each other. The simulation is especially effective at helping students understand how distance and mass are related to orbit. Scroll down on the page for related lesson plans developed by middle school and high school teachers. *Requires Flash*

**Item Type:**Interactive Simulation

**Level:**Grades 7-12

**Duration:**One class period

#### Content Support For Teachers:

This set of materials pertaining to Kepler's laws includes equations and properties of conic sections, scale of the solar system, the energy equation for Keplerian motion, and Newton's "Universal Gravitation". It is part of a larger collection that offers lesson plans, lecture materials, and historical background. No calculus is introduced.

**Item Type:**Historical Reference

**Level:**High School

### Special Collections (2)

#### Lesson Plans:

This page contains procedures for setting up 20 demonstrations relating to motion. All demos have been fully tested in the classroom and were selected for inclusion because they are engaging, require minimal set-up, and are highly illustrative of key concepts taught in introductory classical mechanics. Historical anecdotes and commentary add to the depth of this unique resource.

**Item Type:**Demonstration

**Level:**Grades 6-12

**Duration:**10-20 minutes each

#### References and Collections:

This collection of short videos explores the basic physics of football in a way that's sure to spark interest among kids. Each video features an NFL player, file footage of games, slow-motion video captured with a super high-speed Phantom Cam. Physicists appear in each video to explain the concepts and clarify the connection to physics. Topics: Newton's Laws, momentum, inertia, vectors, center of mass, projectile motion, and more.

**Item Type:**Video Collection

**Level:**Grades 7-12

### Assessments (3)

#### Assessment:

This comprehensive worksheet may be used as a test-quiz for introductory physics or as a diagnostic assessment for more advanced courses. It was designed to accompany the lecture and lesson materials by the same authors (see above under Vectors: Lesson Plans). May be freely downloaded and printed for classroom use.

**Item Type:**Assessment/Problem Set

**Level:**High School

**Duration:**One Class Period

This comprehensive self-assessment offers much more than a set of problems. For each of the 37 questions, links are provided to additional explanations. This resource is ideal for self-assessment or as guided practice for learners who are struggling.

**Item Type:**Self Assessment

**Level:**Grades 9-12

**Duration:**45-60 minutes

Here is a set of free assessment tools for grades 6-12 on topics related to physics and biology. Within the sub-topic of Force and Motion, you'll find assessments to gauge understanding of kinematics, the relationship of motion and force, and momentum. Diagnoser assessments are aligned with the NGSS, and include elicitation (warm-ups) and developmental lessons. After completing the lesson, students answer digital question sets on specific topics, with immediate feedback provided to both teachers and learners. The final step in the process is "Prescriptive Activities", designed to target specific problematic areas located by Diagnoser.

**Item Type:**Assessment Tool

**Level:**6-12

### Modeling Motion (4)

#### Activities:

This simulation is a powerful way to investigate the meaning of shape/slope for 3 types of motion graphs: p-t, v-t, and a-t. Students "match" the motion of a ball whose movement is automatically generated. To do it correctly requires analysis of the motion. Next, learners predict what the graphs will look like by using sliders to generate their own straight-line graphs.

**Item Type:**Interactive Model

**Level:**Grades 9-12

**Duration:**One Class Period

In this model, a ball is launched by a spring-gun in a building with a very high ceiling. The task: calculate an initial velocity so that the ball barely touches the 80-foot ceiling. Students can test their answers by setting the initial velocity on the simulation, then watch the ball's path. Graphs of position vs. time or velocity vs. time can be turned on to view the ball's motion as a function of time.

**Item Type:**Digital Model

**Level:**Grades 10-12

**Duration:**30 minutes

We like the simplicity of this model for introducing free fall and gravitational acceleration. Students can control the initial height, set initial velocity from -20 to 20 m/s and change the gravitational constant. The free fall is displayed as a motion diagram, while graphs are simultaneously displayed showing position, velocity, and acceleration vs. time.

**Item Type:**Digital Model

**Level:**Grades 8-12

**Duration:**One Class Period

Student modeling provides a great opportunity for kids to test and apply their own prototypes to explain and predict physical phenomena. This model includes explicit step-by-step directions for building the computer model with *Easy Java Simulations*, a program that greatly reduces the amount of programming required. It asks students to develop a computer model for a ball moving vertically under the influence of gravity. **Editor's Note**: The activity requires that students have first collected data of a basketball or volleyball bouncing under a motion detector.

**Item Type:**Computer Modeling

**Level:**Grades 9-12

**Duration:**One Class Period