This resource provides explanations and animations that explore the physics of roller coasters. It is designed as a tutorial for either a teacher or learner to be used in conjunction with a unit on amusement park physics. The author uses free-body diagrams and detailed discussion to show how the force of gravity and the normal force act upon the roller coaster as it moves on a straight, curved, or looped track. A short self-test gauges user comprehension. This material is part of the larger Physics Classroom collection.

Editor's Note:Why we like it -- The author gives explicit guidance in understanding circular motion problems, then provides ample opportunities to practice (with solutions provided). Illustrations with force vectors help students understand what each component of an equation represents.

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H4. Whenever one thing exerts a force on another, an equal amount of force is exerted back on it.

9. The Mathematical World

9B. Symbolic Relationships

9-12: 9B/H5. When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes by more than one, and sometimes not at all.

11. Common Themes

11A. Systems

6-8: 11A/M3. Any system is usually connected to other systems, both internally and externally. Thus a system may be thought of as containing subsystems and as being a sub-system of a larger system.

Next Generation Science Standards

Motion and Stability: Forces and Interactions (HS-PS2)

Students who demonstrate understanding can: (9-12)

Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. (HS-PS2-1)

Disciplinary Core Ideas (K-12)

Forces and Motion (PS2.A)

Newton's second law accurately predicts changes in the motion of macroscopic objects. (9-12)

Momentum is defined for a particular frame of reference; it is the mass times the velocity of the object. (9-12)

Definitions of Energy (PS3.A)

Motion energy is properly called kinetic energy; it is proportional to the mass of the moving object and grows with the square of its speed. (6-8)

Conservation of Energy and Energy Transfer (PS3.B)

Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system. (9-12)

Relationship Between Energy and Forces (PS3.C)

When two objects interact, each one exerts a force on the other that can cause energy to be transferred to or from the object. (6-8)

Crosscutting Concepts (K-12)

Cause and Effect (K-12)

Systems can be designed to cause a desired effect. (9-12)

Systems and System Models (K-12)

When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models. (9-12)

Energy and Matter (2-12)

Within a natural or designed system, the transfer of energy drives the motion and/or cycling of matter. (6-8)

Energy cannot be created or destroyed—it only moves between one place and another place, between objects and/or fields, or between systems. (9-12)

NGSS Science and Engineering Practices (K-12)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

Use mathematical representations of phenomena to describe explanations. (9-12)

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.1 Make sense of problems and persevere in solving them.

High School — Algebra (9-12)

Seeing Structure in Expressions (9-12)

A-SSE.2 Use the structure of an expression to identify ways to rewrite it.

Reasoning with Equations and Inequalities (9-12)

A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12

Integration of Knowledge and Ideas (6-12)

RST.11-12.9 Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible.

Range of Reading and Level of Text Complexity (6-12)

RST.9-10.10 By the end of grade 10, read and comprehend science/technical texts in the grades 9—10 text complexity band independently and proficiently.

This resource is part of 2 Physics Front Topical Units.

Topic: Kinematics: The Physics of Motion Unit Title: Circular Motion

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.)

Topic: Dynamics: Forces and Motion Unit Title: Applications of Newton's Laws

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

<a href="http://www.thephysicsfront.org/items/detail.cfm?ID=4809">Henderson, Tom. Physics Classroom: Roller Coasters and Amusement Park Physics. December 12, 2004.</a>

Henderson, T. (2004, December 12). Physics Classroom: Roller Coasters and Amusement Park Physics. Retrieved September 27, 2016, from http://www.physicsclassroom.com/Class/circles/U6L2b.cfm

Henderson, Tom. Physics Classroom: Roller Coasters and Amusement Park Physics. December 12, 2004. http://www.physicsclassroom.com/Class/circles/U6L2b.cfm (accessed 27 September 2016).

%A Tom Henderson %T Physics Classroom: Roller Coasters and Amusement Park Physics %D December 12, 2004 %U http://www.physicsclassroom.com/Class/circles/U6L2b.cfm %O text/html

%0 Electronic Source %A Henderson, Tom %D December 12, 2004 %T Physics Classroom: Roller Coasters and Amusement Park Physics %V 2016 %N 27 September 2016 %8 December 12, 2004 %9 text/html %U http://www.physicsclassroom.com/Class/circles/U6L2b.cfm

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Explore energy conservation and forces for a variety of roller coaster designs at Open Source Physics (OSP). Modify designs and observe the results. Comes with classroom-ready materials.