Lesson Plan | Active Learning | Kinematics: Angular Displacement

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

This stage of the lesson plan is crucial to establish a solid understanding of angular displacement, a fundamental concept in kinematics. By outlining the main objectives, we ensure that students can correctly identify and apply the theory previously studied in practical contexts, which is essential for consolidating learning. This section also serves to align expectations and learning goals for the lesson, preparing the groundwork for the practical activities that will follow.

Main Objectives:

1. Clearly differentiate angular displacement from linear displacement, identifying their distinct characteristics and applications.

2. Enable students to effectively calculate angular displacements using practical examples such as the movement of a clock hand or an object on a circular track.

Side Objectives:

1. Encourage critical thinking among students by exploring the practical and theoretical implications of angular displacement.
2. Develop problem-solving skills in contexts that involve physics calculations.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students with the content they previously studied in a more active and contextualized way. The proposed problem situations encourage students to apply their knowledge to real-world scenarios, preparing them for the practical activities. The contextualization helps to demonstrate the relevance of angular displacement in everyday and professional situations, increasing students' interest and motivation for the subject.

Problem-Based Situations

1. Imagine you are in a go-kart race on a circular track with a diameter of 500 meters. If a driver completes 10 laps, how many meters will they have traveled in total? How does this relate to the concept of angular displacement?

2. Consider a clock hand that moves every 3 minutes. After 30 minutes, in what angular position will the hand be? How can we calculate this angular position and relate it to the concept of displacement?

Contextualization

Angular displacement is not just an abstract concept; it is fundamental in various practical applications, such as in engineering, astronomy, and even in your daily life when using a clock. Interestingly, the sundial is one of the first devices that uses angular displacement to measure time, a clear example of the importance and ubiquity of this concept. Moreover, understanding angular displacement helps to better comprehend phenomena like moon phases, seasons, and even the mechanics of bicycles and cars in curves.

Development

Duration: (70 - 75 minutes)

The Development section is designed to enable students to apply and deepen their prior knowledge of angular displacement in practical and playful contexts. Through engaging and interactive activities, students will have the opportunity to practically experience the theoretical concepts studied, developing calculation skills, logical reasoning, and teamwork. This approach not only solidifies learning but also stimulates curiosity and interest among students in the subject.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - The Pointer Race

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of angular displacement in a practical context, using a simulated clock to calculate and visualize the variation in position of the hands over time.

- Description: In this activity, students will simulate the movement of a clock, calculating and comparing angular displacements of different hands over a period of time. A large circle on the classroom floor will be used, representing the clock face, divided into 12 sections.

- Instructions:

• Divide the class into groups of up to 5 students.

• Each group chooses a clock hand (hour, minute, second).

• Set a starting point for each hand on the circle. Mark this point on the floor.

• Using a stopwatch, start the timer and ask students to calculate the angular displacement of each hand every 5 minutes.

• At each 5-minute interval, students should move the hand on the floor according to the calculation made.

• After 30 minutes, stop the activity and discuss the observed results with the class.

Activity 2 - The Circular Grand Prix

> Duration: (60 - 70 minutes)

- Objective: Use angular displacement to calculate and adjust the speed of an object in circular motion, promoting understanding of the relationship between time, speed, and displacement.

- Description: Students will plan and execute a miniature 'formula race' where small cars will travel around a circular track. The challenge is to calculate and adjust the speed of the cars so that they complete a defined number of laps in a specific time.

- Instructions:

• Organize students into groups of up to 5 people.

• Provide groups with small, lightweight cars, such as toy cars.

• Mark a circular track on the classroom floor with adhesive tape, which will be the 'race track'.

• Groups must calculate the speed necessary for the car to complete 10 laps on the track in 5 minutes.

• After the calculations, each group tests their car on the track, adjusting the speed as needed.

• Conduct a final race to see which group achieved the best approximation of the desired time.

Activity 3 - The Seasons Clock

> Duration: (60 - 70 minutes)

- Objective: Explore angular displacement in an astronomical and practical context, linking solar movement with time measurement and trigonometric concepts.

- Description: In this activity, students will build a simple sundial model and will use the movement of the sun to measure time and calculate shadow angles throughout the day.

- Instructions:

• Divide the class into groups of up to 5 students.

• Provide materials such as a popsicle stick, a string, and a solar marker (or a small flashlight).

• Instruct students to build a 'sundial' by fixing the stick vertically in the ground, with the marker on top.

• Over a period of one hour, groups must record the positions of the shadow projected by the stick at 10-minute intervals.

• Using this data, students must calculate the angular displacements of the shadow and relate them to real time.

• At the end, discuss the variations in angles and the concept of angular displacement involved.

Feedback

Duration: (10 - 15 minutes)

This feedback stage is essential to consolidate students' practical learning and assess their understanding of angular displacement. The group discussion allows students to articulate what they have learned, question each other, and build a deeper collective understanding. Additionally, this exchange of ideas helps the teacher identify which points need to be reviewed or reinforced in the next class.

Group Discussion

At the end of the activities, gather all students for a group discussion. Start the discussion with a brief recap of the activities, highlighting the main objectives of each one. Ask each group to share their findings and the difficulties encountered. Encourage students to discuss how the concepts of angular displacement apply in different situations, both in practical activities and in examples from daily life or theoretical physics.

Key Questions

1. What were the main challenges when calculating and applying angular displacement in the activities conducted?

2. How can understanding angular displacement help solve problems in other areas of physics or even in everyday situations?

3. Was there any situation during the activities where theory did not apply as expected? How was that resolved?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this Conclusion stage is to ensure that students have understood and internalized the key concepts of the lesson, consolidating learning through a review of the main points and a clear demonstration of how theory applies in concrete practices. Furthermore, it reinforces the relevance of the content studied, motivating students to continue exploring and applying the concepts learned in real contexts and future studies.

Summary

To close, the teacher should summarize the main points discussed during the lesson, reiterating the difference between angular and linear displacement and how these concepts were applied in practical activities. It should emphasize the calculations made and the variations observed in angular displacements of different systems, such as the hands of a clock and cars on a circular track.

Theory Connection

During the lesson, the connection between the theory studied and the practical activities was clearly established, allowing students to visualize and calculate angular displacement in real and simulated scenarios. This approach helped to solidify theoretical understanding through direct application, ensuring a deeper comprehension of the concept.

Closing

Finally, it is crucial to highlight the importance of angular displacement in everyday life and in various practical applications, such as in engineering, particle physics, and technology. Understanding this concept not only enriches students' knowledge in physics but also helps them realize its relevance in real and professional situations, stimulating their continued interest in the study of science.