This 10-minute video lesson shows how to figure out the volume of a function rotated about the x-axis .
- Author:
- Khan, Salman
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This 8-minute video lesson looks at the volume of y=sqrt(x) between x=0 and x=1 rotated around x-axis.
- Author:
- Khan, Salman
This 8-minute video lesson examines more volumes around the x-axis.
- Author:
- Khan, Salman
This 9-minute video lesson uses the disk method around the y-axis.
- Author:
- Khan, Salman
This 10-minute video lesson take the revolution around something other than one of the axes.
- Author:
- Khan, Salman
This 4-minute video lesson looks at the last part of the problem in part 7 (see previous video lesson).
- Author:
- Khan, Salman
This 9-minute video lesson uses the \shell method\ to rotate about the y-axis.
- Author:
- Khan, Salman
This 9-minute video lesson shows how to figure out the equation for the volume of a sphere.
- Author:
- Khan, Salman
Students learn about the Foucault pendulum an engineering tool used to demonstrate and measure the Earth's rotation. Student groups create small experimental versions, each comprised of a pendulum and a video camera mounted on a rotating platform actuated by a LEGO MINDSTORMS(TM) NXT motor. When the platform is fixed, the pendulum motion forms a line, as observed in the recorded video. When the rotating, the pendulum's motion is observed as a set of spirals with a common center. Observing the patterns that the pendulum bob makes when the platform is rotating provides insight as to how a full-size Foucault pendulum operates. It helps students understand some of the physical phenomena induced by the Earth's rotation, as well as the tricky concept of how the perception of movement varies, depending on one's frame of reference.
- Author:
- AMPS GK-12 Program,
- Violet Mwaffo and Jeffrey Laut, NYU Polytechnic School of Engineering
Read the Fine Print
Why does the Moon not always look the same to us? Sometimes it is a big, bright, circle, but, other times, it is only a tiny sliver, if we can see it at all. The different shapes and sizes of the slivers of the Moon are referred to as its phases, and they change periodically over the course of a lunar month, which is twenty-eight days long. The phases are caused by the relative positions of the Earth, Sun, and Moon at different times during the month.
- Subject:
- Applied Science
- Astronomy
- Engineering
- Physical Science
- Material Type:
- Activity/Lab
- Lesson Plan
- Author:
- Catie Liken
- Engineering K-PhD Program,
- Teresa Tetlow
- Date Added:
- 09/18/2014
Students work in teams of two to discover the relative positions of the Earth, Sun and Moon that produce the different phases of the Moon. Groups are each given a Styrofoam ball that they attach to a pencil so that it looks like a lollipop. In this acting-out model exercise, this ball on a stick represents the Moon, the students represent the Earth and a hanging lightbulb serves as the Sun. Students move the "Moon" around them to discover the different phases. They fill in the position of the Moon and its corresponding phase in a worksheet.
- Author:
- Engineering K-PhD Program,
- Catie Liken
- Teresa Tetlow
As part of a design challenge, students learn how to use a rotation sensor (located inside the casing of a LEGO® MINDSTORMS ® NXT motor) to measure how far a robot moves with each rotation. Through experimentation and measurement with the sensor, student pairs determine the relationship between the number of rotations of the robot's wheels and the distance traveled by the robot. Then they use this ratio to program LEGO robots to move precise distances in a contest of accuracy. The robot that gets closest to the goal without touching the toy figures at the finish line is the winning programming design. Students learn how rotational sensors measure distance, how mathematics can be used for real-world purposes, and about potential sources of error due to gearing when using rotation sensor readings for distance calculations. They also become familiar with the engineering design process as they engage in its steps, from understanding the problem to multiple test/improve iterations to successful design.
- Author:
- GK-12 Program, Computational Neurobiology Center,
- Nishant Sinha, Pranit Samarth, Satish S. Nair
Conditional Remix & Share Permitted
CC BY-NC-SA
First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.
- Subject:
- Functions
- Mathematics
- Material Type:
- Full Course
- Textbook
- Author:
- Dubowsky, Steven
- Trumper, David L.
- Date Added:
- 01/01/2005
This 9-minute video lesson provides an an introduction to torque.
- Author:
- Khan, Salman
This 14-minute video lesson provides and introduction to moments.
- Author:
- Khan, Salman
Tbhis 14-minute video lesson looks at two more moment problems.
- Author:
- Khan, Salman
Students learn the concept of angular momentum and its correlation to mass, velocity and radius. They experiment with rotation and an object's mass distribution. In an associated literacy activity, students use basic methods of comparative mythology to consider why spinning and weaving are common motifs in creation myths and folktales.
- Author:
- Ben Heavner
- Malinda Schaefer Zarske
- Integrated Teaching and Learning Program,
- Sabre Duren
- Denise Carlson
Students solidify their understanding of the terms "circumference" and "rotation" through the use of LEGO MINDSTORMS(TM) NXT robotics components. They measure the circumference of robot wheels to determine how far the robot can travel during one rotation of an NXT motor. They sharpen their metric system measurement skills by precisely recording the length of a wheel's circumference in centimeters, as well as fractions of centimeters. Through this activity, students practice brainstorming ways to solve a problem when presented with a given scenario, improve their ability to measure and record lengths to different degrees of precision, and become familiar with common geometric terms (such as perimeter and rotation).
- Author:
- AMPS GK-12 Program,
- Ursula Koniges
Conditional Remix & Share Permitted
CC BY-NC-SA
This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity.
- Subject:
- Mathematics
- Trigonometry
- Material Type:
- Full Course
- Textbook
- Author:
- Wuensch, Bernhardt
- Date Added:
- 01/01/2005
This activity teaches students on how the day and night occurs. It also teaches the student about the rotation of the Earth and what two people from opposite sides of the world experience at the same time.
- Author:
- Rogel Mari Sese, Regulus Space Tech