Performance Task - Austin ISD

Name_________________________________________________________ Date __________

Chapter

10 Performance Task

Circular Motion

Instructional Overview

Launch Question

What do properties of tangents tell us about the forces acting on a satellite orbiting around Earth? How would the path of the satellite change if the force of gravity were removed?

Summary

Students use the fact that the radius of a circle is perpendicular to a tangent of the circle at the endpoint of the radius to understand circular motion.

Teacher Notes

Students may struggle with the fact that in circular motion, velocity is actually perpendicular to acceleration. They may assume that it is opposite to the inward force of acceleration. When they spin on a merrygo-round, they "feel" that they are being pulled outward away from the merry-go-round instead of forward, tangent to the merry-go-round. It may be easier for them to understand this with an example like a satellite orbiting Earth or a rock spinning in a sling. The perpendicular relationship is the reason that the rock will fly forward or the satellite will spin into space when the acceleration force is removed.

Supplies

Handouts

Mathematical Discourse

What images come to mind when you hear the word "perpendicular"? Why is a satellite in orbit not one of those images?

Writing/Discussion Prompts What other examples of circular motion can you think of?

Copyright ? Big Ideas Learning, LLC All rights reserved.

Geometry 145

Assessment Book

Name _________________________________________________________ Date _________

Chapter

10

Performance Task (continued)

Circular Motion

Curriculum Content

TEKS Content Standards

Mathematical Thinking

G.5.A, G.12.A

1. A. Apply mathematics to problems arising in everyday life, society, and the workplace. Students discover that the perpendicular relationship between a tangent and radius of a circle occurs in circular motion of objects and predict the paths of objects when their inward forces are removed.

Rubric

Circular Motion

Points

In Exercises 1?4, the path of each object is straight forward in a line that is tangent to its original circular path.

8 Total possible points

2 for each problem answered correctly

Mathematical Thinking:

Apply mathematics to problems arising in everyday life, society, and the workplace. Students discover that the velocity of an object in circular motion is tangent to its circular path, just as the Tangent Line to Circle Theorem (Theorem 10.1) describes the relationship between a line perpendicular to the endpoint of a radius of a circle. They will investigate how this applies to several different real-life scenarios, including a satellite orbiting around Earth.

2 The student explains how the path of an object in circular motion will always be tangent to the circular path when the inward force is removed. Partial credit can be awarded.

Total Points 10 points

146 Geometry

Assessment Book

Copyright ? Big Ideas Learning, LLC All rights reserved.

Name_________________________________________________________ Date __________

Chapter

10

Performance Task (continued)

Circular Motion

What do the properties of tangents tell us about the forces acting on a satellite orbiting around Earth? How would the path of the satellite change if the force of gravity were removed?

A satellite orbiting Earth is an example of an object in uniform circular motion. In this type of motion, an object travels around the perimeter of a circle at a constant speed as an acceleration force pulls it toward the center of the circle. For the satellite, this acceleration is the force of gravity.

The key to the circular path is the relationship between the acceleration and the velocity of the object, which is the speed and direction it is moving. In this case, the force of the acceleration acts like the radius of the circle. To maintain a circular path, the velocity and acceleration must be perpendicular. This means that the velocity of an object in circular motion is tangent to its circular path, just as the Tangent Line to Circle Theorem (Theorem 10.1) describes the relationship between a line perpendicular to the endpoint of a radius of a circle.

If the inward force of acceleration is removed, the object will continue to move in the direction of its velocity. It will fly off in a straight line that is tangent to its circular path.

Using what you know about circles, tangents, and circular motion, describe the path of the following objects.

Copyright ? Big Ideas Learning, LLC All rights reserved.

Geometry 147

Assessment Book

Name _________________________________________________________ Date _________

Chapter

10

Performance Task (continued)

1. To build momentum, an athlete spins 1.5 times through a circle before throwing a discus. The inward force on the discus points toward the body of the athlete. Describe the path of the discus as the athlete releases it.

2. You attach a ball to a string and swing it in a horizontal circle. The tension of the string points inward toward your hand as you spin it. Describe the path of the ball if the string breaks.

148 Geometry

Assessment Book

Copyright ? Big Ideas Learning, LLC All rights reserved.

Name_________________________________________________________ Date __________

Chapter

10

Performance Task (continued)

3. You ride a spinning merry-go-round and hold tightly to the bar. The spinning causes a force on your body that points inward toward the center of the merry-go-round. Describe the path of your body if you release your grip.

4. A skateboarder rides around the lip of a round bowl. The circular path creates a force on the boarder and board that points toward the center of the bowl. Describe the path of the skateboard if the wheels slip completely above the lip of the bowl and the boarder does not change his or her direction.

Copyright ? Big Ideas Learning, LLC All rights reserved.

Geometry 149

Assessment Book

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