**Physical Sciences K-8:** 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.

### Frames of Reference (1)

#### Activities:

This animation takes the fear out of reference frames, and it's fun. All motion is relative to a frame of reference. This resource shows how the motion of a bouncing basketball looks different depending on whether the observer is standing still, walking in the same direction as the player, or walking in the opposite direction. It offers students nine scenarios (*frames of reference*), and they must answer questions from the observer's viewpoint.

**Item Type:**Interactive Simulation

**Level:**Grades 6-12

**Duration:**30 minutes

### Graphing (13)

#### Lesson Plans:

An excellent lesson plan developed specifically to accompany the PhET simulation "The Moving Man". Students with little prior knowledge of graph interpretation will gain understanding of velocity vs. time graphs and how they differ from position vs. time. Adaptable for both middle school and high school.

**Item Type:**Lesson Plan

**Level:**Grades 8-12

**Duration:**One class period

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.

**Item Type:**Teaching Module

**Level:**Grades 8-12

**Duration:**2 Class Periods

Students will apply knowledge of motion by making their own animated sequences that model real-life physical situations. Sound a little zany? Topics include motion in an inertial reference frame, gravity on a falling body, and orbital motion of planets. Fun and creative!

**Item Type:**Project-Based Learning

**Level:**Grades 6-12

**Duration:**3-4 Class Periods

#### Activities:

With one mouse click, students may create their own customized graphs from among five types: bar, line, area, pie, and X/Y. Various patterns, colors, grids, and label choices allow for customization, with a full tutorial to help in set-up. This resource is cost-free.

**Item Type:**Graph-Making Tool

**Level:**Grades 4-12

Blend a motion sensor lab with student-generated graph modeling. Students use the online graph sketching tool to predict the motion of a person walking back & forth over a 40-meter line. Next, they do a motion sensor lab to collect actual data. Last, they analyze differences between their predictions and the real-world data. *Pair this lab with the one directly below, "Motion on a Ramp" for a great 3-day experience.*

**Item Type:**Blended Learning Lab

**Level:**Grades 5-9

**Duration:**1-2 Class Periods

This activity blends a motion sensor lab with digital graph modeling. Students use the online graph-sketching tool to predict graphs of distance vs. time and velocity vs. time. Next, they use a motion sensor to collect data on a real toy being pushed up a ramp. Last, they analyze differences between their predictions and the actual data. *Highly recommended by the editors. For beginners, try first introducing the activity directly above.*

**Item Type:**Blended Lab and Modeling

**Level:**Grades 6-9

**Duration:**1-2 Class Periods

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

This interactive graphing activity explores the effects of gravity on light and heavy objects. It gives learners a means to make predictions, quickly compare their predictions with real data, and analyze why the predictions were right or wrong. It's one of the few resources we've seen in which universal gravitation, constant acceleration, slope of the line, and graphing of free-fall motion can all be meaningfully explored in one class period. Includes lesson plan & assessment w/answer key.

**Item Type:**Digital Model

**Level:**Grades 6-12

**Duration:**One Class Period

#### References and Collections:

This set of lessons investigates the language of kinematics (the physics of motion). It is designed to help students understand that the scientific meaning of words like "velocity" and "acceleration" is different from their use in everyday language.

**Item Type:**Interactive Tutorial

**Level:**Grades 8-12

**Duration:**20 minutes

#### 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:

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

#### Assessment:

An assessment designed by the award-winning Modeling Instruction team. It assesses a student's ability to create and also interpret motion maps, p-t graphs, and v-t graphs. Could be used either as a class review or as a unit test. Downloadable in pdf format.

**Item Type:**Assessment

**Level:**Grades 8-12

**Duration:**One Class Period

An assessment in the form of a question that asks students to identify which objects are accelerating, when shown a set of four strobe diagrams. A2L materials are designed to reveal what students do NOT know and build a basis for formative assessment.

**Item Type:**Formative Assessment

**Level:**Grades 7-12

**Duration:**10 minutes

### Vectors (7)

#### Activities:

It can be difficult for beginning students to understand what a vector represents. This fun simulation allows them to watch vectors change as they drive a virtual car. Speed vs. Time is also displayed in a real-time companion graph.

**Item Type:**Scaffolded Simulation

**Level:**Grades 7-10

**Duration:**30 minutes

This very simple simulation can help beginners understand what vector arrows represent. It was designed by the PhET team to target specific areas of difficulty in student understanding of vectors. Learners can move a ball with the mouse or let the simulation control the ball in four modes of motion (two types of linear, simple harmonic, and circular). Two vectors are displayed -- one green and one blue. Which color represents velocity and which acceleration?

**Item Type:**Interactive Simulation

**Level:**Grades 6-12

**Duration:**20-30 minutes

#### Content Support For Teachers:

The primary goal of the Kinematics Graphing Project is to investigate the ability of students to interpret kinematics graphs and to generate a set of suggestions for faculty teaching the subject.

**Item Type:**Research

**Level:**Teacher Support

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. Great background information for teachers.

**Item Type:**Reference Material

**Level:**Teacher Support

This award-winning web tutorial is a great choice for the crossover teacher who wants a refresher on vectors and their properties. Included is an introduction to free-body diagrams, example problems, a series of self-paced questions, and related interactive simulations.

**Item Type:**Interactive Tutorial

**Level:**Teacher Support

#### Student Tutorials:

This simple, yet effective Java-based tutorial uses geometric overlays to demonstrate why the Pythagorean Theorem works. Background text helps students understand its importance in vector algebra.

**Item Type:**Simulation-based Tutorial

**Level:**Grades 8-12

**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

### Motion in One Dimension (8)

#### Lesson Plans:

In this inquiry-based lesson plan for grades K-2, students record data as they roll different objects down a ramp whose height is variable. It is the first of a two-part lesson on ramps and their mechanical advantages.

**Item Type:**Lesson Plan

**Level:**Grades K-2

**Duration:**40 minutes

This project-based lesson for grades K-2 is designed as a follow-up to Ramps 1 (see item above.) In this activity, students experiment with a variety of materials as they design, build, and test their own ramps. Included is a printable student data sheet.

**Item Type:**Lesson Plan

**Level:**Grades K-2

**Duration:**One hour

#### 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. *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 interactive graphing activity explores the effects of gravity on light and heavy objects. It gives learners a means to make predictions, quickly compare their predictions with real data, and analyze why the predictions were right or wrong. It's one of the few resources we've seen in which universal gravitation, constant acceleration, slope of the line, and graphing of free-fall motion can all be meaningfully explored in one class period. Includes lesson plan & assessment w/answer key.

**Item Type:**Digital Model

**Level:**Grades 6-12

**Duration:**One Class Period

#### References and Collections:

A must-read for teachers of K-8 science and 9th grade physical science. A physics education researcher studied groups of students in grades 4, 6, and 8. The research took a deep look at how students at these grade levels distinguish between speed and changing speed. The findings will help teachers in constructing effective lessons. *Editor's Note: Why is this Important? Research reveals that children in elementary school form and maintain conceptions about the physical world that remain deeply entrenched into adulthood. Inaccurate conceptions can be very difficult to reverse.*

**Item Type:**Research Article

**Level:**Teacher Support

#### Content Support For Teachers:

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 takes beginners through a full conceptual analysis before introducing the math. It was developed using principles of physics education research. Appropriate for gifted/talented middle school students.

**Item Type:**Interactive Tutorial

**Level:**Grades 8-12

**Duration:**30-40 minutes

### Motion in More Than One Dimension (5)

#### Lesson Plans:

An excellent two-day lesson to accompany the PhET simulation *Projectile Motion* (see Activities below). It was crafted by educators to provide robust support to both teachers and learners on projectile motion with and without air resistance. You will find scripted teacher discussion, explanations of fluid properties of air, and modifiable worksheets. *Created for middle school, but can be easily adapted to Physics First or Physics Prep courses.*

**Item Type:**Lesson Plan

**Level:**Grades 6-9

**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

#### Content Support For Teachers:

Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. The goal of any study of kinematics is to develop sophisticated mental models which serve to describe (and ultimately, explain) the motion of real-world objects.

**Item Type:**Interactive Tutorial

**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

### Circular Motion (5)

#### Activities:

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

Can an amusement park Merry-Go-Round be designed to be dangerous? This simple model lets kids discover for themselves how rotational speed and radial distance interact to create a more thrilling ride. Don't miss the page link to "Physiological impact of G-forces". Setting the speed & radial distance at the highest points will result in g-forces that exceed space shuttle re-entry and high speed fighter jets!

**Item Type:**Interactive Simulation

**Level:**Grades 6-12

**Duration:**20-30 minutes

This very simple simulation explores both conservation of energy and circular motion. A roller coaster travels over a large and small hill, then goes through a loop. Students can have fun controlling speed, height of the hills, and size of the loop, then viewing the effect on the moving car. *No mathematics is introduced.*

**Item Type:**Interactive Simulation

**Level:**Grades 6-12

**Duration:**20-30 minutes

#### 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 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)

#### Lesson Plans:

This 40-minute lesson, created by a veteran high school teacher, gives kids explicit guidance in using the PhET simulation *My Solar System* to explore orbital motion and gravitational attraction. Great concept building activity.

**Item Type:**Simulation-Based Lesson

**Level:**Grades 8-10

**Duration:**One Class Period

#### Activities:

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.

**Item Type:**Interactive Simulation

**Level:**Grades 7-12

**Duration:**One class period

How did scientists first directly demonstrate that the Earth rotates? This short video, seen through the eyes of a child, explores the work of French scientist Leon Foucault -- a pendulum seems to rotate as it swings, but there is no external force that would cause the rotation (clockwise in the Northern Hemisphere, counterclockwise in the Southern). Through experiments, Foucault showed that it's not the pendulum doing the rotating. It's the steady, predictable movement of the Earth's rotation on its axis.

**Item Type:**Video Clip

**Level:**Grades 3-6

### Special Collections (5)

#### 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

This 8-day instructional unit for middle school integrates engineering practice into a study of the energy of motion. Through investigations of waterwheels, roller coasters, bouncing balls, and a pendulum, students get a solid introduction to energy transformation in a mechanical system. The unit also introduces static and kinetic friction, drag, elastic/inelastic collision, and students learn to calculate frictional force. *Don't have time to do the full unit? Lessons can be pulled out individually.*

**Item Type:**Instructional Unit

**Level:**Grades 6-8

**Duration:**8-10 Class Periods

#### Activities:

This free collection will impress teachers in the way it promotes depth of understanding about graphs. Learners use interactive digital tools to predict how a motion graph will look, then they watch as the computer simulates process in real time. Next, they place inputs on the graphs and use language to explain what is happening. Finally, they compare their own predictions with the simulated process to analyze why the graphs appear as they do. As with all Concord Consortium materials, the resources are subjected to rigorous classroom testing to ensure their effectiveness.

**Item Type:**Interactive Tutorials

**Level:**Grades 6-12

An exceptional resource collection on how to integrate "direct measurement videos". These high-speed short videos feature tools for easy analysis of various physical situations: rulers, grids, frame-counters, and screen overlays for making precise measurements. Includes 9 teaching modules with lesson plans, assessments and answer keys, and pedagogical background. *Does not require purchase or installation of video analysis software.*

**Item Type:**Video Analysis Lessons

**Level:**Grades 9-12

#### 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

### Velocity and Acceleration (9)

#### Lesson Plans:

This inquiry-based lesson for grades K-2 is similar to Galileo's classic experiment with inclined planes. Children roll spherical objects of different masses down ramps of varying heights. As they record data, they are building a conceptual base for understanding the constant nature of acceleration due to gravity. See the item below for Part 2 of the lesson.

**Item Type:**Lesson Plan

**Level:**Grades K-2

**Duration:**40 minutes

This project-based lesson for grades K-2 is designed as a follow-up to Ramps 1 (see item above.) In this activity, students experiment with a variety of materials as they design, build, and test their own ramps. Included is a printable student data sheet.

**Item Type:**Lesson Plan

**Level:**Grades K-2

**Duration:**One hour

#### Activities:

This versatile simulation lets students explore the effects of braking on an object moving with constant velocity. Set the initial velocity, start the applet, and hit the brakes. Graphs of velocity vs. time and position vs. time are simultaneously displayed. You can also set the rate of braking acceleration. This resource will help students build concepts relating to frictional force.

**Item Type:**Interactive Simulation

**Level:**Grades 8-12

**Duration:**30 minutes

This robust activity from Concord Consortium lets kids deeply explore the meaning behind the slopes of velocity/time and position/time graphs. It blends interactive graph sketching, data analysis, and digital Q&A as learners explore the motion of an animated car. It will help students understand why motion graphs appear as they do, rather than mimic the pathway of an object's motion.

**Item Type:**Digital Model

**Level:**Grades 6-10

**Duration:**One Class Period

This middle school activity blends a motion sensor lab with a digital "SmartGraph" tool to help learners understand how forward, fast, and slow motions look on a graph of Position vs. Time. The activity requires a Vernier Go! motion device, which provides inputs to the SmartGraph interface via a USB connection.

**Item Type:**Digital Model/Motion Lab

**Level:**Grades 5-9

**Duration:**One Class Period

This activity blends a motion sensor lab with digital *SmartGraph* software to help learners see how the slope of a P/T graph can be used to find velocity. Scaffolding is provided at intervals to help with calculations. Requires a Vernier Go! motion sensing device.

**Item Type:**Motion Lab/Modeling

**Level:**Grades 6-10

**Duration:**One Class Period

This interactive graphing activity explores the effects of gravity on light and heavy objects. It gives learners a means to make predictions, quickly compare their predictions with real data, and analyze why the predictions were right or wrong. It's one of the few resources we've seen in which universal gravitation, constant acceleration, slope of the line, and graphing of free-fall motion can all be meaningfully explored in one class period. Includes lesson plan & assessment w/answer key.

**Item Type:**Digital Model

**Level:**Grades 6-12

**Duration:**One Class Period

#### References and Collections:

A must-read for teachers of K-8 science and 9th grade physical science. A physics education researcher studied groups of students in grades 4, 6, and 8. The research took a deep look at how students at these grade levels distinguish between speed and changing speed. The findings will help teachers in constructing effective lessons. **Editor's Note:** Why is this important? Research reveals that children in elementary school form and maintain conceptions about the physical world that remain deeply entrenched into adulthood. Inaccurate conceptions can be very difficult to reverse.

**Item Type:**Research Article

**Level:**Teacher Support

In this study, students in an inquiry-based classroom were videotaped to detect how they made sense of concepts relating to force and motion. The analysis revealed that focused "sense-making activities", free-body diagrams, energy diagrams, and related real-world activities produced deeper student understanding. *Free download*

**Item Type:**Research Article

**Level:**Teacher Support

### Modeling Motion (1)

#### Activities:

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

### The Case of Roller Coasters (10)

#### Lesson Plans:

Roller coasters offer an inherently interesting way to study energy transformation in a system. This simulation lets students choose from 5 track configurations or create their own design, then watch the resulting motion. Energy bar graphs are simultaneously displayed as the coaster runs its course. Students can adjust the initial speed and friction, or switch to stepped motion to see exact points where kinetic and potential energy reach maximum and minimum levels. *Includes lesson plan and student guide.*

**Item Type:**Simulation-Based Lesson

**Level:**Grades 6-10

**Duration:**One Class Period

Students build understanding of kinetic and potential energy as they design a physical model of a roller coaster with foam pipe insulation and marbles. The lesson is almost completely turn key: scripted teacher introduction, detailed illustrated instructions, student worksheet, scoring rubric, and post-activity assessment. Which track configuration works best? What can be done to reduce friction?

**Item Type:**Lesson Plan

**Level:**Grades 7-9

**Duration:**Two Class Periods

A four-day lesson that explores the same physics concepts as roller coaster design, but breaks the learning into two distinct segments to ensure that beginners understand the basics. In Part I, kids build a very simple curved track to explore kinetic and potential energy for a gumball moving downhill. Part II becomes more complex: build and test a gumball machine with loops and specific design constraints.

**Item Type:**Instructional Module

**Level:**Grades 7-10

**Duration:**4-5 class periods

#### Activities:

This short video does a great job of demonstrating centripetal force and how it acts to keep objects moving along a curved path. What makes a rider on a roller coaster feel a sensation of being thrown outward from the center during a loop, although there is no outward net force? The video serves to help beginners understand the dynamics of circular motion.

**Item Type:**Video Clip

**Level:**Grades 7-12

**Duration:**5 minutes

Exactly what IS centripetal force and what does it do? An astronaut on board the International Space Station demonstrates this force in ways students cannot observe in daily life. The environment is "almost" weightless, making it easy to observe the center-seeking motion without the complicating effects of gravity.

**Item Type:**Video Clip

**Level:**Grades 6-12

**Duration:**5 minutes

Want to do a quick lesson on energy transfer in a roller coaster, but can't devote more than one class period? This simulation lets kids design a very simple roller coaster, then it evaluates the design based on physical principles, safety, and "fun factor". Good springboard for further inquiry into energy transformation.

**Item Type:**Interactive Simulation

**Level:**Grades 6-10

**Duration:**30 minutes

This self-paced multimedia tutorial explores how cars move along a roller coaster track as a result of energy transformation. Part of the Middle School Literacy Project, it is designed to develop literacy skills in the context of a focused science or math lesson. Students read informational text, build vocabulary, view videos and interactive simulations, and create written responses in both short and extended forms. Registered teachers may set up student accounts for tracking progress.

**Item Type:**Multimedia Tutorial

**Level:**Grades 6-9

**Duration:**30 minutes

#### References and Collections:

The heart of this website for engineering education is its wonderful collection of videos that feature kids doing activities that illuminate key concepts in science and engineering. Each video is well-produced to allow the actor-students to apply concepts of science, then experience the excitement that goes with real discovery. Here's a taste: one video takes kids on a field trip to the Etnies shoe headquarters to learn the biomechanics of skateboarding from engineers who are also skateboarders. Another video takes the kids to Epcot Center to design and plan their own roller coaster configurations. The site also offers interactive games and simulations.

**Item Type:**Digital Collection

**Level:**Grades 6-10

#### Content Support For Teachers:

If you need a refresher in the basics, this is a nicely organized tutorial that addresses four topics: uniform circular motion, centripetal force, applications and mathematics of circular motion, and amusement park physics. Includes free-body diagrams, animations, and problem sets with answers.

**Item Type:**Interactive Tutorial

**Level:**Introductory Physics

Short tutorial that uses an animation to illustrate the work/energy relationship in a roller coaster. The author breaks down the associated equation to show how total mechanical energy is conserved in the system.

**Item Type:**Interactive Tutorial

**Level:**Introductory Physics