Objectives (5 - 7 minutes)

1. Understand the concept of Angular Displacement: Students should be able to understand what angular displacement is, how it is measured, and how it relates to the rotation of an object. This includes the ability to differentiate between angular displacement and the distance traveled on a curved path.

2. Apply the formula for Angular Displacement: Students should be able to apply the formula for angular displacement to solve problems and calculate the angular displacement of a rotating object.

3. Recognize the unit of measure for Angular Displacement: Students should be able to identify and use the correct unit of measure for angular displacement, which is the radian.

Secondary Objectives:

• Develop problem-solving skills: In addition to learning the concept and formula for angular displacement, students should be able to apply this knowledge to solve problems, thus developing their logical and mathematical reasoning skills.

• Promote active learning: Through practical activities and classroom discussions, students will be encouraged to actively engage in the learning process, promoting a deeper and lasting understanding of the topic.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing the concepts of kinematics, especially the concepts of rotation and angle. This can be done through a brief theoretical review or by asking students questions to verify if they remember these concepts. This review is crucial for students to understand the new concept of angular displacement. (3 - 5 minutes)

2. Problem situation 1: The teacher can propose the following situation: 'Imagine an object rotating around an axis. How can we measure how much this object has moved along its circular path?' This question serves to stimulate students' curiosity and to introduce the concept of angular displacement. (2 - 3 minutes)

3. Contextualization of the importance of the subject: The teacher should then explain the importance of angular displacement in various areas, such as physics, engineering, astronomy, and even in everyday activities, like measuring the number of turns a bicycle wheel has made. This will help motivate students to understand and learn the subject. (2 - 3 minutes)

4. Theory of situation 1: The teacher can then explain that angular displacement is a measure of how much an object has moved along a circular path. They should emphasize that angular displacement is measured in radians, which is the standard unit for measuring angles in physics. The teacher can illustrate this with practical examples, such as the movement of the hands of a clock. (2 - 3 minutes)

5. Problem situation 2: To further pique students' interest, the teacher can propose a second situation: 'Imagine you are on a Ferris wheel. How can we measure how much you have moved along the Ferris wheel? And if you moved backwards, how would that be measured?' This problematic situation will help consolidate the concept of angular displacement and differentiate it from linear distance traveled. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Modeling Activity with String and Pencil (10 - 12 minutes):

   • Required materials: String of at least 1 meter in length and a pencil.
   • Divide the class into groups of up to 4 students. Each group will receive a string and a pencil.
   • Explain that the activity consists of modeling angular displacement. For this, students must form a circle on the floor with the string and place the pencil in the center of the circle.
   • Students should hold the string with the pencil in the center and then one of the students should pull the string to one side, moving the pencil out of the center of the circle.
   • Students should observe that the pencil moved along the circumference of the circle, but the reference point (the pencil) did not move from the initial position (the center of the circle).
   • Students should discuss and conclude that the pencil underwent an angular displacement, but not a linear displacement.
   • Students should measure the length of the string and use the formula for angular displacement to calculate the distance traveled by the pencil along the circumference of the circle.

2. Angular Displacement and Angular Velocity Activity with Clock (10 - 12 minutes):

   • Required materials: Clock with hands (or a drawing of a clock with movable hands).
   • Still in groups, students will receive a clock with hands (or a drawing of a clock with movable hands).
   • Explain that students should observe the clock and identify the angular displacement of the hands for each passing minute.
   • Students should measure the angular displacement of the hands for different time intervals (for example, 5 minutes, 10 minutes, etc.).
   • Students should discuss and conclude that the angular displacement of the hands is constant, indicating a constant angular velocity.
   • Students should calculate the angular velocity of the clock hands using the formula: angular velocity = angular displacement / time.
   • Students should compare the angular velocities of the clock hands (for example, the minute hand moves more slowly than the hour hand) and discuss what this means in terms of angular displacement and angular velocity.

3. Group Discussion (5 - 7 minutes):

   • At the end of the activities, ask each group to present their conclusions to the class.
   • Encourage students to discuss their observations, difficulties, and learnings during the activities.
   • The teacher should then make the connection between the activities carried out and the theory of angular displacement, reinforcing the concepts learned.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes):

   • The teacher should start the group discussion, inviting each group to share their solutions or conclusions from the activities carried out.
   • Each group should have a maximum of 3 minutes to present their findings, allowing all groups the opportunity to share.
   • During the presentations, the teacher should ask questions to clarify the concepts, encourage the participation of all students, and correct any misunderstandings.

2. Connection between Activities and Theory (2 - 3 minutes):

   • After all presentations, the teacher should recap the activities, highlighting how they connect with the theory of angular displacement.
   • The teacher should emphasize the main concepts, such as the difference between angular displacement and distance traveled on a curved path, the formula for angular displacement, and the unit of measure for angular displacement (radian).
   • The teacher should reinforce the importance of angular displacement in various areas, such as physics, engineering, astronomy, and in everyday activities.

3. Individual Reflection (2 - 3 minutes):

   • After the group discussion, the teacher should suggest that students reflect individually on what they learned in the lesson.
   • The teacher should ask guiding questions, such as: 'What was the most important concept you learned today?' and 'What questions have not been answered yet?'.
   • Students should write down their reflections on a piece of paper or in their notebooks, which can be reviewed in the next lesson or used as a basis for planning future lessons.

4. Closure (1 minute):

   • To conclude the lesson, the teacher should thank the students for their participation, reinforce the importance of continuous study, and encourage them to ask questions and seek clarification whenever necessary.
   • The teacher should also remind students of homework assignments and any additional study materials that may help in understanding angular displacement.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes):

   • The teacher should start the Conclusion by recalling the main points covered during the lesson. This includes the definition of angular displacement, the formula for calculating angular displacement, and the unit of measure, the radian.
   • The teacher should also recap the practical activities carried out, highlighting how they helped illustrate and consolidate the theoretical concepts.
   • Additionally, the teacher should refer to the problem situations presented at the beginning of the lesson, explaining how they were solved based on the knowledge acquired about angular displacement.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes):

   • Next, the teacher should emphasize the importance of the connection between theory, practice, and applications of angular displacement.
   • It should be highlighted how the practical activities allowed students to apply theory in a concrete way, helping to reinforce the understanding of the concept.
   • The teacher can also mention some of the applications of angular displacement in everyday life and in various areas of knowledge, reinforcing the relevance of the subject.

3. Additional Materials (1 minute):

   • The teacher should then suggest additional study materials for students who wish to deepen their knowledge of angular displacement.
   • These materials may include textbooks, educational videos, physics websites, and simulation apps.
   • The teacher should emphasize that reviewing these materials can be helpful for understanding future topics related to kinematics.

4. Importance of the Subject (1 minute):

   • To conclude, the teacher should reinforce the importance of angular displacement for everyday life and for various areas of knowledge.
   • The teacher can cite practical examples, such as measuring turns on a bicycle wheel, predicting eclipses in astronomy, or analyzing rotational movements in machines and equipment in engineering.
   • The teacher should encourage students to see physics as a relevant and applicable discipline, capable of explaining and describing various phenomena present in the world around us.