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Applied mathematics Mathematics Science Vocational guidance Technology MathematicsFilter By Series
Math in a boxFilter By Subjects
Applied mathematics Mathematics Science Vocational guidance Technology MathematicsFilter By Series
Math in a boxSummary: This program considers the idea that circular motion must imply a force or component of a force toward the center of a circle, as in the Newtonian theory of how the Moon orbits the Earth. The reasons why bicyclists lean during turns, why roads are banked, and why car tires react as they do during a turn are investigated.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: In this program, resonance is examined. The value of mathematical models is demonstrated through the physics of applying a time-varying force to a body that fundamentally exhibits simple harmonic motion. Solution techniques for general linear second-order differential equations are featured.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: This program shows that a single mathematical model can describe the takeoff of a wide variety of aircraft, running the gamut from a single-engine trainer to the Concorde. Because the search for approximations is somewhat complex, graphical notation is employed to reveal the interaction and variation of the forces involved.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: After explaining the principle of moments, this program shows how apparently dissimilar physical phenomena are actually mathematically similar through the examples of a synthetic heart valve, a lock gate, and the gymnastic maneuver known as a flic-flac, or back handspring. The need to make careful approximations during the modeling process is stressed.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: Employing diverse examples such as trains and water slides, this program illustrates the use of vectors to represent forces operating in both two and three dimensions. The algebraic manipulation of vectors in modeling problems is featured.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: In this program, geometry is combined with approximation to solve relatively complex problems involving shooting an arrow and landing an airplane on the deck of an aircraft carrier. Emphasizing the value of sketching as a visualization tool, the program also explains how the solution of the archery problem, through geometric inversion, can help solve the problem of a plane landing.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: In this program, animated graphics help to define the concept of angular momentum and to express the relationship between moments and the rate of change of angular momentum. Problems include determining the dimensions needed for an airplane's ailerons and the amount of force required to rotate a toy spaceship. The reasons why a spinning top shows precession are also addressed.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: Using Newton's second law and a balloon-powered toy car, this program examines how impulse relates to the change in momentum and how the rate of that change equates to the resultant force. In addition, the exhaust velocity of the jet-propelled car is estimated.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: After defining the basic concepts of vectors, this program uses algebra to determine how the resultant of numerous forces acting on a body can be obtained and then equated to the product of mass and acceleration. Kites are employed to exemplify both equilibrium and non-equilibrium conditions.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: This program introduces the concept of simple harmonic motion through the operation of the pendulum. The findings of Galileo and his contemporaries on the mechanics of the pendulum are presented, along with examples of pendular motion drawn from the modern world.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: This program investigates how the mathematical model of simple harmonic motion becomes more complex through the introduction of damping. The application of simple modeling techniques to create homogeneous linear second-order differential equations is illustrated.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: This program uses a parachutist to demonstrate the effects of drag on the force of gravity, showing how to make mathematical approximations and how the resultant forces can be equated to the product of mass and acceleration. A first-order differential equation is then used to find the minimum height from which a parachutist can jump without injury.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: In this program, footage of rockets blasting off and avalanches roaring down mountainsides provides two perspectives of the same principle: the rate of change of momentum. Practical calculations of the time it takes for a rocket to lift off and the time a skier has to escape a landslide, plus an experiment with eggs and flour, reinforce the lesson.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: This program discusses how geometry, gravity, and the coefficient of friction determine whether an object slides or topples. The mathematical models behind these phenomena are presented through examples such as ice hockey and skiing. The relationship between sliding and a body's velocity as an exercise in energy conservation is explored as well.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006
View online at AVOD
Summary: Moving beyond the concept of simple force, this program expands the application of vectors to include velocity, acceleration, and rotational motion. In addition, moments of greater complexity are investigated through vector geometry. Real-world examples are included.
Format: software, multimedia
Publisher / Publication Date: Films Media Group 2006