Contextualization

Theoretical Introduction

Angular displacement is a fundamental concept in physics that describes movement around a central point. This idea is crucial for understanding phenomena such as the rotation of the Earth or the movement of a clock hand.

Unlike linear displacement, which refers to how a point moves from one place to another in a straight line, angular displacement considers the rotation of a point around a central axis. In other words, it involves the change in orientation of a radius or reference line.

Angular displacement is commonly measured in radians, which is the ratio between the distance traveled along the circumference and its radius. This is an international standard used in various areas of science and engineering.

Contextualization

Angular displacement is a concept with very important practical applications. For example, in the motor vehicle industry, analyzing the angular displacement of rotating parts, such as the engine, can help improve vehicle performance.

Furthermore, angular displacement is a key essential to understanding the principles governing astronomy. For example, the movement of planets around the sun is described using angular displacement.

With this in mind, the ability to understand and calculate angular displacement is a fundamental skill for any physics student. Not only will it allow them to better understand the world around them, but it will also open doors to careers in a wide range of fields.

Activity

Activity Title: Construction of a Sundial

Project Objective

Apply the theoretical concepts of angular displacement in the construction of a simple sundial, enabling a better understanding and visualization of this phenomenon in our daily lives.

Detailed Project Description

In this project, students will build a simple model of a sundial, which allows observing the change in the sun's angular displacement throughout the day, based on the projected shadow. Part of the challenge will be to make the necessary measurements and correlate the angles measured with the time of day.

Groups should consist of 3 to 5 students, with a recommended total of 5 to 10 hours of dedicated work per student.

Required Materials

• Ruler
• Pencil or pen
• Cardboard or cardstock
• Protractor
• Compass
• Tape

Step-by-Step Guide for the Activity

1. Locate the central point of the cardboard or cardstock and make a mark with the pencil.
2. Use the ruler to draw a straight line from the center to the edge of the cardboard.
3. Use the compass to align the line with True North.
4. Attach a pen or pencil at a 90-degree angle to the surface of the cardboard at the central point where the mark was made.
5. Place the constructed model in an area that receives sunlight throughout the day.
6. Monitor and record the shadow's position every hour. To do this, make a mark where the pencil's shadow hits the drawn line.
7. From these marks, draw lines representing each hour of the day, using the protractor to measure the angular displacement between each one.
8. Determine the relationship between angular displacement and time, creating a function that describes this relationship.

Project Deliverables

After completing the practical part, each group must prepare a report detailing the entire activity carried out.

The report should follow the following structure:

1. Introduction: In this section, students should contextualize the project theme, providing a brief theoretical review of angular displacement and its importance in practice. Additionally, they should mention the project's objective and the relevance of the proposed experiment.

2. Development: Here, students should explain step by step the activity carried out, describing the materials used, the measurements taken, and the calculations performed. Additionally, the results obtained and observations made during the experiment should be presented. It is important for students to justify the choices made during the project execution and discuss the possible associated errors.

3. Conclusion: In this final section, students should summarize the main points of the work and discuss whether the proposed objectives were achieved. They should also mention the lessons learned during the project and their impressions of the activity.

4. Bibliography: Finally, students should indicate the sources consulted for the project's elaboration.

The report must be submitted within one month after the project's start.