Objectives (5 - 10 minutes)

1. Grasp the concept of angular displacement: This objective aims for students to understand the definition of angular displacement, which is the measure of the change in the position of a point moving around an axis. Students should be able to differentiate between angular displacement and angular velocity.

2. Apply the formula for angular displacement: Students should learn to apply the formula for angular displacement (θ = s/r) to calculate the angular displacement of an object in circular motion. They should be able to solve problems involving the determination of angular displacement.

3. Identify and calculate the number of revolutions: In addition to calculating angular displacement, students should be able to identify and calculate the number of complete revolutions an object makes over a given period of time. This involves understanding that one revolution corresponds to an angle of 2π radians.

Secondary objectives:

• Develop critical thinking: Through solving problems involving angular displacement, students should develop critical thinking skills, such as the ability to analyze, synthesize, and evaluate information.

• Stimulate interest in Physics: By presenting the concept of angular displacement clearly and relating it to practical examples, the lesson aims to spark students' interest and appreciation for Physics.

Introduction (10 - 15 minutes)

1. Review of Previous Concepts: The teacher begins the lesson by recalling the concepts of circular motion and angular velocity, which were studied in previous lessons. They can ask students questions to check their retention of these concepts. For example, "What is circular motion?" or "How would you differentiate between angular velocity and angular displacement?". (3 - 5 minutes)

2. Problem Situation: The teacher presents two problem situations that involve the concept of angular displacement. The first situation could be: "Imagine the hand of a clock that is at the 3 o'clock position. If it moves to the 6 o'clock position, what was its angular displacement?". The second situation could be: "If you make 10 complete revolutions around a circle, what is your angular displacement?". These situations serve to stimulate students' curiosity and prepare them for the introduction of the topic. (4 - 6 minutes)

3. Contextualization: The teacher presents the importance of angular displacement in various areas of everyday life and science. They could mention, for example, that angular displacement is used in engineering to design rotating components, such as motors and gears. Additionally, they could explain that angular displacement is fundamental to understanding natural phenomena, such as the rotation of the Earth and the orbit of planets. (2 - 4 minutes)

4. Introduction of the Topic: The teacher introduces the topic by explaining that angular displacement is the measure of the change in the position of a point moving around an axis. They could use an analogy, such as that of the hand of a clock, to facilitate the understanding of the concept. Additionally, the teacher could mention that angular displacement is measured in radians, a unit of measurement widely used in physics. (2 - 4 minutes)

Development (20 - 25 minutes)

1. Theory - Angular Displacement (5 - 7 minutes):

   • The teacher should begin by explaining that angular displacement is the measure of the change in the position of a point moving around an axis.
   • They should emphasize that angular displacement is different from linear displacement, which is the change in the position of an object in a straight line.
   • The teacher should clarify that angular displacement is measured in radians, which is a unit of measurement widely used in physics.

2. Theory - Formula for Angular Displacement (5 - 7 minutes):

   • The teacher should then introduce the formula for angular displacement (θ = s/r), where θ is the angular displacement, s is the arc length traveled, and r is the radius of the circle.
   • They should explain that the arc length traveled is the distance along the circumference and the radius is the distance from the point of rotation to the point that is moving.
   • The teacher should provide examples of how to use the formula to calculate angular displacement. For instance, if an object travels an arc of 2 meters on a circle with a radius of 1 meter, the angular displacement is 2 radians.

3. Theory - Number of Revolutions (3 - 5 minutes):

   • The teacher should explain that one complete revolution corresponds to an angle of 2π radians.
   • They should demonstrate how to calculate the number of complete revolutions an object makes over a given period of time.
   • The teacher should provide examples of how to calculate the number of revolutions. For instance, if an object makes an angular displacement of 6π radians, this corresponds to 3 complete revolutions.

4. Practice - Examples of Applications (5 - 6 minutes):

   • The teacher should present examples of how angular displacement is applied in practice.
   • They could mention, for example, that angular displacement is used in engineering to design rotating components, such as motors and gears.
   • The teacher should encourage students to think of other situations where angular displacement can be applied.

5. Practice - Problem Solving (2 - 3 minutes):

   • The teacher should then propose some problems for students to solve.
   • The problems should involve calculating angular displacement and the number of revolutions.
   • The teacher should guide students in solving the problems step by step and clarify any doubts that may arise.

Feedback (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): The teacher should promote a group discussion about the solutions to the problems presented in the practice stage. They can ask some students to share their solutions with the class, and then open the floor for questions and comments. This will help to reinforce the concepts learned and clarify any doubts that students may have.

2. Connection with the Theory (3 - 5 minutes): The teacher should then make the connection between the theory and the practice, explaining how the concepts of angular displacement and the number of revolutions were applied to solve the proposed problems. They should emphasize that understanding the theory is essential for effective problem-solving in practical situations.

3. Individual Reflection (2 - 3 minutes): The teacher should ask students to reflect silently for a minute on what they have learned in the lesson. They can then ask the following questions to guide students' reflection:

   1. "What was the most important concept you learned today?"
   2. "What questions are still unanswered for you?"
   3. "How can you apply what you learned today to everyday situations or other subjects?"

4. Sharing of Reflections (1 - 2 minutes): The teacher should then ask some students to share their reflections with the class. This will allow students to learn from each other and for the teacher to better understand the individual learning needs of the class.

5. Teacher Feedback (1 - 2 minutes): Finally, the teacher should provide feedback on the lesson, highlighting the strengths and areas for improvement. They should reinforce the key concepts that were learned and encourage students to continue practicing and reviewing the material at home. The teacher can also suggest additional resources, such as supplementary readings or educational videos, to help students deepen their understanding of the topic.

Conclusion (5 - 7 minutes)

1. Summary of the Content (1 - 2 minutes): The teacher should begin the Conclusion by summarizing the main points covered in the lesson. They should reinforce that angular displacement is the measure of the change in the position of a point moving around an axis, and that it is calculated using the formula θ = s/r, where θ is the angular displacement, s is the arc length traveled, and r is the radius of the circle. The teacher should also remind students that one complete revolution corresponds to an angle of 2π radians.

2. Connection Between Theory and Practice (1 - 2 minutes): The teacher should then highlight how the lesson connected theory, practice, and application. They should explain that, through the examples and exercises, students were able to apply the formula for angular displacement and calculate the number of revolutions. The teacher should emphasize that understanding the theory is essential for effective problem-solving in practical situations.

3. Supplementary Materials (1 - 2 minutes): The teacher should suggest additional study materials for students, such as supplementary readings, educational videos, or websites with interactive simulations. For example, they could recommend a video that explains angular displacement in a visual and intuitive way, or a website that allows students to practice solving problems related to the topic.

4. Relevance of the Topic (1 - 2 minutes): Finally, the teacher should emphasize the importance of angular displacement in everyday life and in various areas of science and technology. For example, they could mention that angular displacement is used in engineering to design rotating components, such as motors and gears. Additionally, they could explain that angular displacement is fundamental to understanding natural phenomena, such as the rotation of the Earth and the orbit of planets. The teacher should end the lesson by reaffirming the relevance of studying Physics and encouraging students to continue exploring and questioning the world around them.