• 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)

• The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. (6-8)
• Newton's second law accurately predicts changes in the motion of macroscopic objects. (9-12)

• Patterns in rates of change and other numerical relationships can provide information about natural systems. (6-8)

• 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)

• Obtaining, evaluating, and communicating information in 9–12 builds on K–8 and progresses to evaluating the validity and reliability of the claims, methods, and designs. (9-12)
  • Communicate scientific information (e.g., about phenomena and/or the process of development and the design and performance of a proposed process or system) in multiple formats (including orally, graphically, textually, and mathematically). (9-12)

• 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)

• 6-8: 4F/M3b. If a force acts towards a single center, the object's path may curve into an orbit around the center.
• 9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

• 9-12: 9B/H1b. Sometimes the rate of change of something depends on how much there is of something else (as the rate of change of speed is proportional to the amount of force acting).
• 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.

• N-VM.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

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

• 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.
• F-IF.8.b Use the properties of exponents to interpret expressions for exponential functions.
• F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

• RST.9-10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
• RST.11-12.2 Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms.

• 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.

• RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11—CCR text complexity band independently and proficiently.

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.

• Physics First Circular Motion Unit
• Conceptual Physics Circular Motion Unit
• Algebra-Based Physics Circular Motion Unit
• AP/Calculus-Based Physics Circular Motion Unit

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.

• Physical Sciences K-8 The Case of Roller Coasters Unit
• Physics First The Case of Roller Coasters Unit

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.

• Physics First Rotational Dynamics Unit
• Conceptual Physics Rotational Dynamics Unit
• Algebra-Based Physics Rotational Dynamics Unit
• AP/Calculus-Based Physics Rotational Dynamics Unit