This lesson challenges students to apply their knowledge of object motion by animating sequences of hand-rendered pictures that model a set of physical conditions. The challenges include animating the orbital motion of planets and satellites, the effects of gravity on a falling body, and motions of objects in inertial (moving) frames of reference. The lesson was created by a high school physics teacher to help learners build quantitative reasoning skills in preparation for understanding kinematics.
Editor's Note:Modeling is a powerful way for students to relate the math formula to the physical process under study. This lesson allows learners to develop hand-crafted "flipbook" models of motion before they advance to computer modeling. In each challenge, data is provided so the animations can be computationally accurate.
Metadata instance created
June 12, 2004
by Cathy Ezrailson
February 2, 2013
by Caroline Hall
AAAS Benchmark Alignments (2008 Version)
2. The Nature of Mathematics
2A. Patterns and Relationships
9-12: 2A/H1. Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world.
2C. Mathematical Inquiry
9-12: 2C/H2. Much of the work of mathematicians involves a modeling cycle, consisting of three steps: (1) using abstractions to represent things or ideas, (2) manipulating the abstractions according to some logical rules, and (3) checking how well the results match the original things or ideas. The actual thinking need not follow this order.
4. The Physical Setting
6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.
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/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.
9-12: 4F/H2. All motion is relative to whatever frame of reference is chosen, for there is no motionless frame from which to judge all motion.
9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.
4G. Forces of Nature
6-8: 4G/M1. Every object exerts gravitational force on every other object. The force depends on how much mass the objects have and on how far apart they are. The force is hard to detect unless at least one of the objects has a lot of mass.
6-8: 4G/M2. The sun's gravitational pull holds the earth and other planets in their orbits, just as the planets' gravitational pull keeps their moons in orbit around them.
11. Common Themes
9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.
9-12: 11B/H5. The behavior of a physical model cannot ever be expected to represent the full-scale phenomenon with complete accuracy, not even in the limited set of characteristics being studied. The inappropriateness of a model may be related to differences between the model and what is being modeled.
Common Core State Standards for Mathematics Alignments
Standards for Mathematical Practice (K-12)
MP.4 Model with mathematics.
High School — Functions (9-12)
Interpreting Functions (9-12)
F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.?
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.
This resource is part of a Physics Front Topical Unit.
Topic: Kinematics: The Physics of Motion Unit Title: Graphing
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!
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