Students learn how forces are used in the creation of art. They come to understand that it is not just bridge and airplane designers who are concerned about how forces interact with objects, but artists as well. As "paper engineers," students create their own mobiles and pop-up books, and identify and use the forces (air currents, gravity, hand movement) acting upon them.

The EJS Baton Throw model displays a baton thrown up in the air about its center of mass. The baton is modeled by two masses separated by massless rigid rod. The path of the center of mass of the baton and the red mass are shown in black and red, respectively. The ratio of the two masses can be set via a slider and the initial velocity of the center of mass of the baton and the rotational velocity of the baton can be set via text boxes.

The Body with Thruster Model shows the motion of a disk with an attached rocket engine. You can drag the engine to change its distance from the center of the disk and you can adjust the thrust of the rocket engine using sliders. The mass of the rocket and its connecting rod are assumed to be negligible. The trajectory of this single-body model is intuitively challenging and difficult to visualize.

This activity allows children to construct something themselves and be creative while learning about the concept of the center of mass.

This Internet resource provides introductory information, concept or skill development in Mathematics for grade 9, 10, 11, and 12 students who are at grade level in a single student situation. This text was initially written by David Guichard. The single variable material (not including infinite series) was originally a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. New material has been added, and old material has been modified, so some portions now bear little resemblance to the original.

This digital textbook was reviewed for its alignment with California content standards.

The Colliding Galaxies Model is an implementation of Alar and Juri Toomres' 1972 super computer model showing the formation of galactic bridges and tails under the assumption that galactic cores are point masses and that one galactic core is surrounded by 2D concentric rings of orbiting stars. The model assumes is that the stars (test particles) orbiting the galactic cores are non-interacting. When the two galaxies pass one another, tidal forces deform the star distribution into classic tidal features. Our EJS model reproduces this result showing that there is a long curving tail and that only the outermost ring of stars is affected by its companion galaxy. A thin bridge is also formed and some of the stars are captured by the companion galactic core.

Investigate collisions on an air hockey table. Set up your own experiments: vary the number of discs, masses and initial conditions. Is momentum conserved? Is kinetic energy conserved? Vary the elasticity and see what happens.

Counterweights can be useful to stabilize a small robot, and to aid in the movement of its parts.

This activity can be used to explore forces acting on an object, to practice graphing experimental data, and/or to introduce the algebra concepts of slope and intercept of a line. A wooden 2x4 beam is set on top of two scales. Students learn how to conduct an experiment by applying loads at different locations along the beam, recording the exact position of the applied load and the reaction forces measured by the scales at each end of the beam. In addition, students will analyze the experiment data with the use of a chart and a table and model linear equations to describe relationships between independent and dependent variables.

The application of engineering principles is explored in the creation of mobiles. As students create their own mobiles, they take into consideration the forces of gravity and convection air currents. They learn how an understanding of balancing forces is important in both art and engineering design.

Students explore the concepts of center of mass and static equilibrium by seeing how non-symmetrical objects balance. Using a paper cut-out shape of a parrot sitting on a wire coat hanger, they learn that their parrot exists in stable equilibrium it returns to its balancing point after being disturbed. The weight of its tail makes the parrot balance upright. Give the parrot a push, and she knocks off balance, but swings back and forth until coming to rest in balance again.

This 10-minute video lesson provides an introduction to the center of mass. [Physics playlist: Lesson 64 of 164].

The concepts of stability and equilibrium are introduced while students learn how these ideas are related to the concept of center of mass. They gain further understanding when they see, first-hand, how equilibrium is closely related to an object's center of mass. In an associated literacy activity, students learn about motion capture technology, the importance of center of gravity in animation and how use the concept of center of gravity in writing an action scene.

NBC's Lester Holt looks at how the physics concepts of torque and center of mass are applied in football by some of the games most massive players — the offensive linemen. "Science of NFL Football" is a 10-part video series funded by the National Science Foundation and produced in partnership with the National Football League.

To learn about the concept of center of mass, students examine how objects balance. They make symmetrical cut-outs of different "creatures" and experiment with how they balance on a tightrope of string. Students see the concept of center of mass at work as the creatures balance.

This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.