Students work as physicists to understand centripetal acceleration concepts. They also learn about a good robot design and the accelerometer sensor. They also learn about the relationship between centripetal acceleration and centripetal force governed by the radius between the motor and accelerometer and the amount of mass at the end of the robot's arm. Students graph and analyze data collected from an accelerometer, and learn to design robots with proper weight distribution across the robot for their robotic arms. Upon using a data logging program, they view their own data collected during the activity. By activity end , students understand how a change in radius or mass can affect the data obtained from the accelerometer through the plots generated from the data logging program. More specifically, students learn about the accuracy and precision of the accelerometer measurements from numerous trials.

Students analyze the relationship between wheel radius, linear velocity and angular velocity by using LEGO(TM) MINDSTORMS(TM) NXT robots. Given various robots with different wheel sizes and fixed motor speeds, they predict which has the fastest linear velocity. Then student teams collect and graph data to analyze the relationships between wheel size and linear velocity and find the angular velocity of the robot given its motor speed. Students explore other ways to increase linear velocity by changing motor speeds, and discuss and evaluate the optimal wheel size and desired linear velocities on vehicles.

Video tutorial uses examples to reinforce understanding of how to find the area of a circle. [2:48]

Biology 2e is designed to cover the scope and sequence requirements of a typical two-semester biology course for science majors. The text provides comprehensive coverage of foundational research and core biology concepts through an evolutionary lens. Biology includes rich features that engage students in scientific inquiry, highlight careers in the biological sciences, and offer everyday applications. The book also includes various types of practice and homework questions that help students understand—and apply—key concepts. The 2nd edition has been revised to incorporate clearer, more current, and more dynamic explanations, while maintaining the same organization as the first edition. Art and illustrations have been substantially improved, and the textbook features additional assessments and related resources.

By the end of this section, you will be able to do the following:

Discuss the different types of skeletal systems
Explain the role of the human skeletal system
Compare and contrast different skeletal systems

Solve two challenging problems that apply properties of tangents to find the radius of a circle with a tangent.

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Students expand their knowledge of circles to establish relationships between angle measures in and around circles, line segments and lines in and around circles, and portions of circles as related to area and circumference.

Given this lesson and either the diameter or radius of a circle, you'll be able to calculate the other measure.

A great site to find general information on stars and their place in the universe. Click on the topics on the right margin for additional information about stars.

Through this lesson and its two associated activities, students are introduced to the use of geometry in engineering design, and conclude by making scale models of objects of their choice. The practice of developing scale models is often used in engineering design to analyze the effectiveness of proposed design solutions. In this lesson, students complete fencing (square) and fire pit (circle) word problems on two worksheets—which involves side and radius dimensions, perimeters, circumferences and areas—guiding them to discover the relationships between the side length of a square and its area, and the radius of a circle and its area. They also think of real-world engineering applications of the geometry concepts.

In this science activity you will examine circular objects and see what you can discover about their sizes. As you explore, you might be surprised at how useful the results can be -- maybe it will inspire you to save up for a bike with bigger wheels!

In this video segment [3:10] from Cyberchase, the CyberSquad must find the exact center of a circle in order to save Motherboard.

This discussion examines how to complete the square in circle equations. Students learn about the math concept through definitions and examples with detailed solutions.

Students work as engineers and learn to conduct controlled experiments by changing one experimental variable at a time to study its effect on the experiment outcome. Specifically, they conduct experiments to determine the angular velocity for a gear train with varying gear ratios and lengths. Student groups assemble LEGO MINDSTORMS(TM) NXT robots with variously sized gears in a gear train and then design programs using the NXT software to cause the motor to rotate all the gears in the gear train. They use the LEGO data logging program and light sensors to set up experiments. They run the program with the motor and the light sensor at the same time and analyze the resulting plot in order to determine the angular velocity using the provided physics-based equations. Finally, students manipulate the gear train with different gears and different lengths in order to analyze all these factors and figure out which manipulation has a higher angular velocity. They use the equations for circumference of a circle and angular velocity; and convert units between radians and degrees.

Students apply algebraic and proportional reasoning skills to investigate angle relationships, circle measurements, uniqueness of triangles, and solid figure application problems.

Students practice their multiplication skills using robots with wheels built from LEGO® MINDSTORMS® NXT kits. They brainstorm distance travelled by the robots without physically measuring distance and then apply their math skills to correctly calculate the distance and compare their guesses with physical measurements. Through this activity, students estimate parameters other than by physically measuring them, practice multiplication, develop measuring skills, and use their creativity to come up with successful solutions.

Students explore in detail how the Romans built aqueducts using arches—and the geometry involved in doing so. Building on what they learned in the associated lesson about how innovative Roman arches enabled the creation of magnificent structures such as aqueducts, students use trigonometry to complete worksheet problem calculations to determine semicircular arch construction details using trapezoidal-shaped and cube-shaped blocks. Then student groups use hot glue and half-inch wooden cube blocks to build model aqueducts, doing all the calculations to design and build the arches necessary to support a water-carrying channel over a three-foot span. They calculate the slope of the small-sized aqueduct based on what was typical for Roman aqueducts at the time, aiming to construct the ideal slope over a specified distance in order to achieve a water flow that is not spilling over or stagnant. They test their model aqueducts with water and then reflect on their performance.

Working as a team, students discover that the value of pi (3.1415926...) is a constant and applies to all different sized circles. The team builds a basic robot and programs it to travel in a circular motion. A marker attached to the robot chassis draws a circle on the ground as the robot travels the programmed circular path. Students measure the circle's circumference and diameter and calculate pi by dividing the circumference by the diameter. They discover the pi and circumference relationship; the circumference of a circle divided by the diameter is the value of pi.