**AP/Calculus-Based Physics:** Dynamics: Forces and Motion Units

A branch of mechanics that deals with forces and their relation primarily to motion but also sometimes to the equilibrium of bodies. Units are not listed in a prescribed order.

### Newton's First Law & Inertia (14)

#### Lesson Plans:

This unique lesson helps students understand that inertia is an inherent property of matter, while weight depends on gravity. Using simple and inexpensive objects, students make mass measurements without the use of gravity, similar to the measurements made aboard the Skylab space mission.

**Item Type:**Lesson Plan

**Level:**Grades 8-12

Auto collisions offer a concrete way to think about inertia in motion. In this PBL activity, students must figure out who is at fault in a T-bone collision, given little more than the extent of seat-belt laceration injuries of one driver. The student guide may be freely accessed; registration is required to download the teacher's guide with lesson plan. *Note: **The Student Guide is freely accessible. To access an answer key, teachers may contact the author.*

**Item Type:**Problem-Based Lesson

**Level:**Grades 9-12

**Duration:**1-2 Class Periods

#### Activities:

This full lab manual encourages critical thinking by using the Socratic Method of inquiry. Students must consider opposing and contradictory views, engage in active dialog about given problems, and defend their own conclusions. This lab covers Newton's First Law (inertia) and Third Law (action/reaction).

**Item Type:**Lab

**Level:**Grades 9-12

Great classroom activity to get students thinking about the Law of Inertia, force interactions, and conservation of momentum as they solve a real-life problem to determine which driver is at fault in a car accident. See link below under Content Support to read more about the pedagogy behind Problem-Based Learning.

**Item Type:**Problem-Based Learning

**Level:**Grades 9-12

Cool classroom demo for illustrating inertia at rest. A dollar bill is placed between two soda bottles; the top bottle is filled with water. Upward/downward forces are balanced because the dollar acts as a sealant. Quickly removing the dollar bill creates a net unbalanced force on the water, which whooshes into the soda bottle below. *Try teaming this teacher-led demo with the Pencil Drop below, which students could perform.*

**Item Type:**Demonstration

**Level:**Grades 6-12

A great companion to the "Dollar Bill Grab" above. This demo illustrates the same basic concept (Law of Inertia). If done correctly, it looks like a magic trick. Even if done incorrectly, it still demonstrates the idea of inertia at rest. Could be a good springboard for cooperative learning groups to discuss the meaning of net force, and what happens when net force is zero.

**Item Type:**Demonstration

**Level:**Grades 6-12

What would happen if an object in circular motion suddenly loses its net centripetal force? Teachers can easily set up this demo to show students that Newton's Law of Inertia will govern the situation, and the object will fly off in a straight line tangential to the circular path.

**Item Type:**Interactive Demonstration

**Level:**Grades 6-12

This simulation shows an airplane flying at constant horizontal velocity preparing to drop relief supplies to a small island. As captain of the plane, the student must calculate the release point for dropping the package. *Students may insist that there is a horizontal force acting upon the package since it has a horizontal motion. Actually, the horizontal motion of the dropped package results from its inertia.*

**Item Type:**Interactive Simulation

**Level:**Grades 9-12

#### Content Support For Teachers:

Problem-Based Learning (PBL) is an instructional method that presents authentic, life-like situations to engage students in learning. Click here to read more about the pedagogical basis of PBL and how to implement it in the physics classroom. This site also features several PBL scenarios developed for introductory physics students (many are appropriate for high school).

**Item Type:**Pedagogy

**Level:**Secondary teachers

This chapter from *The Book of Phyz* offers curriculum support for teaching about the Law of Inertia. It features well-written background information for teachers, related activities and experiments.

**Item Type:**Content Support

**Level:**Secondary teachers

#### Student Tutorials:

Beginning students gain an in-depth, yet entertaining view of the background and applications of the Law of Inertia. Through animations and self-guided problems, this tutorial helps students understand the idea of unbalanced force and see that mass is a measure of the amount of inertia.

**Item Type:**Web-based Tutorial

**Level:**Introductory Physics

#### Assessment:

An assessment to help teachers determine whether students understand the relationship between mass and inertia. This alternative homework problem, based on physics education research, presents students with a real-life situation about highway stopping distance and the related physics.

**Item Type:**Performance Assessment

**Level:**Grades 11-12

A simulation-based problem to spark student discussion about inertia and force interactions. A puck traveling on a frictionless air hockey table is given a momentary push. What is the resulting path of its motion? *Pair this applet with the one below on sustained push. Assesses student understanding of how resultant motion is affected by the type of force applied.*

**Item Type:**Formative Assessment

**Level:**Grades 6-12

A simulation-based problem that supplements the problem above on momentary push. A satellite is floating at constant velocity when its thrusters engage. The resulting path of its motion will differ from the example above. *Assesses student understanding of how resultant motion is affected by a sustained force produced by thrust.*

**Item Type:**Formative Assessment

**Level:**Grades 6-12

### Newton's Second Law & Net Force (6)

#### Activities:

This model simulates an air track glider, a low-friction device commonly used to conduct experiments on Newton's Second Law and collisions. It features a two-mass system connected by a string. Change the value of either mass or the coefficient of friction on the track.....and watch the effects on the motion. *Available in HTML5 or Java.*

**Item Type:**Interactive Simulation

**Level:**Grades 9-12

Students are challenged to measure the mass of a car using only bathroom scales, measuring tape, stopwatch, position markers, and a Vernier caliper. They are provided keys to the car but may not start it. They work cooperatively to apply principles of kinematics, Newton's Second Law, and kinetic friction. True to the PBL method, there is more than one strategy for solution. A printable student guide is provided. Registered teacher-users can also access a free instructor's guide.

**Item Type:**Problem-Based Learning

**Level:**High School Physics

**Duration:**4-5 Class Periods

This simulation lets students explore force interactions, motion graphs, and friction at a broad range of levels. Choose from 5 objects of different masses, select a wood or ice surface, then "push" the object on a straight path. You can display force vectors, free body diagrams, and graphs of position, acceleration, and velocity vs. time. Record your "push" and play it back to see the sum of forces. *For more advanced students: set gravitation to mimic the Moon or Jupiter and watch the effects on static and kinetic friction!*

**Item Type:**Interactive Simulation

**Level:**Grades 6-12

#### References and Collections:

How do beginners use and interpret FB diagrams? Do these symbolic representations help novice physics learners become better problem-solvers? This article from *Physics Review Special Topics* gives detailed results of a 2009 study. A key result: students who "draw diagrams correctly are significantly more successful in obtaining the right answer for the problem". Read full article for more insight. (Free download)

**Item Type:**Physics Educ. Research

#### Student Tutorials:

This four-part tutorial takes an up-close look at the meaning of forces, how we determine net force, and the use of free-body diagrams to represent force interactions. Don't miss the Gravitational Fields widget to investigate how location affects the value of the gravitational constant! *Highly recommended by the editors.*

**Item Type:**Interactive Tutorial

**Level:**Grades 9-12

This interactive homework problem presents an object with 3 forces acting on it. Learners must find the magnitude of the net force with the information given. The author provides explicit help with correct placement of the vectors to calculate net force, then leads them interactively through the calculations. Immediate feedback is received for both correct and incorrect responses. *This problem incorporates principles of PER (Physics Education Research).*

**Item Type:**Interactive Problem

**Level:**9-12

**Duration:**30 minutes

### Newton's Third Law (1)

#### Activities:

This full lab manual encourages critical thinking by using a "Socratic Method" of inquiry. Students must consider opposing and contradictory views, engage in active dialog about given problems, and defend their own conclusions. This lab covers Newton's First Law (inertia) and Third Law (action/reaction).

**Item Type:**Laboratory

**Level:**Grades 11-12

**Duration:**Two Class Periods

### Applications of Newton's Laws (5)

#### Lesson Plans:

A lesson for exploring the physics & engineering of artificial heart valves. Students examine and operate both a ball valve and a gate valve, then they work as a team of "engineers" to develop and sketch enhancements to the mechanical heart valve. Great activity for integrating engineering design in the secondary classroom.

**Item Type:**Lesson Plan

**Level:**Grades 8-12

**Duration:**Two Class Periods

#### Activities:

Move objects of varying mass along a 1-D path and watch as the simulation displays graphs of position vs. time, velocity vs. time, and acceleration. Applied force, friction, and gravitational constants can be varied in this interactive activity. *Can be adapted for use in either middle or high school.*

**Item Type:**Interactive Simulation

**Level:**Grades 7-12

This set of activities developed by the Exploratorium offers students an engaging 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.

**Item Type:**Classroom Activity/Videos

**Level:**Grades 9-12

Robust set of 21 problems (with detailed solutions) to give students deep practice in motion, force interactions, and momentum. You can view each problem separately or download as a pdf file. The questions were carefully crafted to align with best practices in physics education. The resource follows the pedagogy of the *Matter and Interactions* instructional method, which emphasizes student modeling and integration of modern physics into a standard curriculum.

**Item Type:**Question/Answer Set

**Level:**Grades 10-12

#### References and Collections:

This resource directs teachers in the set-up of 20 engaging demonstrations relating to motion/mechanics. The materials include motion in one and two dimensions, coupled pendulum motion, rotational motion, and more. The author selected each demonstration for its "attention-getting" appeal and its ability to provoke thought about specific mechanical processes.

**Item Type:**Classroom Demonstration

**Level:**Grades 6-12

### The Universal Law of Gravitation (2)

#### Lesson Plans:

This lesson plan, developed for teaching Newton's formulation of gravity, recreates a single calculation that validates Newton's result. It is intended to help students appreciate the philosophical implication of Newton's calculation: all parts of the universe seem to obey the same laws of nature.

**Item Type:**Lesson Plan

**Level:**High School Physics

#### Content Support For Teachers:

This resource features well-organized text explanations alongside equations in a concept-building format for understanding gravitational interactions. Short problems and tables provide a concrete approach to helping learners grasp the universal nature of gravitational attraction so that formulas make sense.

**Item Type:**Interactive Tutorial

**Level:**High School Physics

### Frictional Forces (4)

#### Activities:

Applying the skills of teamwork, students work cooperatively to find out coefficients of friction for surfaces of metal on wood and metal on metal.

**Item Type:**Lesson Plan

**Level:**Grades 9-12

This simulation demonstrates motion of a block being pulled up an incline plane at constant velocity by a spring. By changing the angle of inclination, mass, and coefficient of friction, students can better understand how frictional force affects the movement of an object on a hill. *Available in HTML5 or Java.*

**Item Type:**Interactive Simulation

**Level:**Grades 8-12

Students are challenged to measure the mass of a car using only bathroom scales, measuring tape, stopwatch, position markers, and a Vernier caliper. They are provided keys to the car but may not start it. They work cooperatively to apply principles of kinematics, Newton's Second Law, and kinetic friction. True to the PBL method, there is more than one strategy for solution. A printable student guide is provided. Registered teacher-users can also access a free instructor's guide.

**Item Type:**Problem-Based Learning

**Level:**High School Physics

**Duration:**4-5 Class Periods

This model, newly converted to HTML5, provides a highly visual way for students to investigate friction in a system of a skateboarder moving on a track. It begins with an idealized system (no friction) with bar graph showing changes in kinetic and potential energy as the skater moves along the track. Click "Friction" to set frictional force from low to high. As friction is introduced to the system, thermal energy is displayed alongside PE and KE in the bar graph. Students can readily see how friction affects the motion of the skater.

**Item Type:**Interactive Simulation

**Level:**6-12

**Duration:**30 minutes

### Force Diagrams (1)

#### References and Collections:

How do beginners use and interpret FB diagrams? Do these symbolic representations help novice physics learners become better problem-solvers? This article from *Physics Review Special Topics* gives detailed results of a 2009 study. A key result: students who "draw diagrams correctly are significantly more successful in obtaining the right answer for the problem". Read full article for more insight. (Free download)

**Item Type:**Physics Educ. Research

### Rotational Dynamics (4)

#### Activities:

This item is a fun demonstration using an ordinary bicycle wheel and rotating stool to illustrate conservation of angular momentum. A person sits on the stool and spins a bicycle wheel on a hand-made axis. The person twists the spinning wheel, and the rotating stool also begins to turn. The author provides a full explanation of the physics involved.

**Item Type:**Demonstration

**Level:**Grades 9-12

#### 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 resource, 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 9-12

#### 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:**High School Physics

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:**Grades 9-12

### Benchmarks and Standards (1)

#### References and Collections:

This resource is the Forces of Nature section of the Science Literacy Benchmarks published by the American Association for the Advancement of Science (AAAS). It is a statement of desired learning outcomes on the topic of physical forces and interactions for grades 2, 5, 8, and 12.