Contextualization

When we observe an object with circular motion, such as a cart on a roller coaster or a clock hand, we can notice that the time it takes to complete a full circle is always the same. This constancy is defined as the period of motion, a key concept in Physics that will be the focus of our project. To understand more deeply, let's initially divide the circumference into angles and analyze circular motion, both uniform and varied, and their characteristics.

Studying the period in circular motions is fundamental to understand everyday phenomena and modern technologies. It is present in the movements of planets, in tidal cycles, in electric motors, and even in the cycles of our computer processors. In-depth knowledge on the subject is important for the education of a Physics student, as it opens doors to the understanding of more complex concepts, such as electromagnetic waves.

Understanding what the period of motion and frequency are helps to understand the relationship between these two quantities. Did you know that frequency is the inverse of the period? This is a simple mathematical relationship, but quite useful. Mastering this topic allows us to predict the behavior of various systems that oscillate or rotate, from a simple pendulum to a particle accelerator.

Satellites orbiting the Earth, for example, have a defined rotation period. This is precisely calculated so that the satellite can fulfill its function, whether it is transmitting TV or internet signals, weather forecasting, scientific research, among others. We can also relate the theme to the generation of electrical energy. In generators, the circular motion of their parts is what allows the transformation of mechanical energy into electrical energy.

To study the subject, we suggest the following sources of research:

1. "Fundamentals of Physics: Gravitation, Waves, and Thermodynamics - Volume 2" - Authors: David Halliday, Robert Resnick, and Jearl Walker. Chapter 6 - Circular Motion.
2. "Basic Physics Course - Volume 1" - Author: H. Moysés Nussenzveig. Chapter 10 - Circular Motion.
3. Website "Mundo Educação" - Uniform Circular Motion.
4. Website "Brasil Escola" - Circular Motion.
5. YouTube Channel "Interactive Physics" - Uniform Circular Motion (UCM) - Frequency, Period.

Practical Activity

Activity Title: "Spinning in Circles: A Study on the Period of Circular Motions"

Project Objective

The objective of this project is to allow students to explore the concept of period in circular motions through a practical and playful activity that stimulates interaction and collaboration among group members. In addition, students will be encouraged to apply theoretical knowledge in a practical way to better understand the concept of period and its importance.

Detailed Project Description

Students will build a simple pendulum and a conical pendulum, also known as a Newton's pendulum, to observe and investigate how the periods of circular motions can be measured and calculated. The group will compare the periods of the two pendulums and relate them to various parameters.

Required Materials

1. String
2. Marble or other small and heavy object
3. Ruler
4. Stopwatch
5. Fixed support (can be a table or a chair)
6. Adhesive tape

Step-by-Step for Activity Execution

Pendulum Construction

1. To build the simple pendulum, tie a piece of string to the marble. The other end of the string will be fixed to the support with adhesive tape. Make sure the string is taut and the marble can move freely.

2. To build the conical pendulum, tie a second piece of string to the same marble of the simple pendulum. The other end of this string will be fixed at a different point on the support, forming an angle with the first string.

3. Use the ruler to measure and record the lengths of the strings.

Observation and Measurement

1. Release the marble of the simple pendulum at a 45-degree angle to the vertical, observing its motion and recording the time required to complete 10 oscillations with the stopwatch. Repeat the process three times to obtain an average time.

2. Do the same for the conical pendulum, releasing the marble and recording the time required to complete 10 full rotations.

3. Calculate the period of each pendulum (simple and conical) by dividing the total time by the number of oscillations or rotations.

After completing the practical activity, groups should produce a report containing:

1. Introduction: Contextualization of the theme and description of the project objectives, as well as its relevance.

2. Development: Theoretical explanation about the period in circular motions and detailed description of the practical activity carried out. Include the methodology used, the data collected, calculations performed, and results obtained.

3. Conclusion: Discussion on the results obtained, project learnings, and the relationship of the studied theme with the real world.

4. Bibliography: Reference to the resources used for the project.

This project should be carried out by groups of 3 to 5 students, with an estimated workload of 3 hours per student and a delivery time of one week after the project presentation. Remember, the goal of the project is to promote the understanding of the concept of period in circular motions, as well as to develop technical and socio-emotional skills, such as teamwork, problem-solving, critical thinking, among others.