Lesson plan of Kinematics: Uniform Circular Motion Acceleration

Objectives (5 - 7 minutes)

1. Understand the concept of acceleration in uniform circular motion and its relation with the angular velocity and the radius of the path.

2. Apply the formula of the acceleration in the uniform circular motion in different problem-situations, in order to calculate the acceleration, the angular velocity, and the radius of the path.

3. Develop problem-solving skills, logical reasoning, and critical thinking, through the application of the concepts of acceleration in uniform circular motion.

Secondary objectives:

• Encourage teamwork and communication among students, through the realization of practical activities in a group.

• Promote the understanding of the relevance and practical applications of the concept of acceleration in uniform circular motion, by linking it to examples from everyday life and technology.

Introduction (10 - 12 minutes)

1. Review of previous concepts:

• The teacher starts the lesson by making a brief review of the concepts of speed and acceleration, highlighting the differences between them and recalling the formulas to calculate each one. They can use practical examples or real-life situations to illustrate these concepts and make them easier for students to understand.

2. Problem situation:

• The teacher presents students with a problem situation: imagine a car on a race track. The car is going around at a constant speed, but, suddenly, its driver steps on the accelerator. What happens to the car? Does it keep going at the same speed, or does it accelerate? Why does that happen?

• Then, the teacher questions the students about the relevance of this phenomenon to our daily lives and technology that we use, like amusement parks, for example.

3. Contextualization:

• The teacher explains that the uniform circular motion, with constant acceleration, is common in many everyday life situations and in many technologies. They can cite examples like Ferris wheels, carousels, roller coasters, and washing machines (during the spinning cycle), among others.

• The teacher also mentions the importance of the study of acceleration in uniform circular motion to the comprehension of more advanced concepts in Physics, like the centripetal force and the conservation of angular momentum.

4. Grabbing attention:

• To spark the students' interest, the teacher can share curiosities or stories related to the subject. For example, they can tell the story of the discovery of the centripetal force by Isaac Newton, and how that discovery revolutionized Physics. Another interesting curiosity is about the simulation of uniform circular motion in video games and action films, which use complex algorithms to calculate the acceleration and the speed of the objects in scene.

• The teacher can also show a short video of a roller coaster in motion, and ask the students what they observe and what they think is happening with the cars.

Development (20 - 25 minutes)

1. Activity 1 - "Car on the Track" (10 - 12 minutes)

• The teacher divides the class into groups of up to 5 students. Each group will receive a toy car, a piece of string, a pencil, and a ruler.

• The activity consists of creating a circular "track" on the classroom floor, using the piece of string. The track should have a radius of approximately 30 centimeters.

• Then, the students should secure the car to the string, in a way that makes it move along the circular track. The pencil should be secured to the rear of the car, so when the car moves, the pencil draws a circle on the floor.

• The teacher instructs students to measure the time it takes the car to make 10 complete laps on the track (using a stopwatch or a phone's clock), and write down the value.

• Next, students should measure the length of the circular trace the pencil drew on the floor. They can use the ruler to do this.

• Finally, students should use the values they got to calculate the angular velocity and acceleration of the car, using the formulas introduced in the lesson. The teacher should walk around the classroom, assisting the groups and clarifying doubts.

2. Activity 2 - "Roller Coaster" (10 - 12 minutes)

• While still in their groups, the students will receive an A4 sheet of paper, a coin, and a pen.

• The activity consists of drawing a "roller coaster" on the paper, using the pen. The roller coaster should have at least three "turns" and one "looping."

• After drawing the roller coaster, the students should place the coin on one of the cars of the roller coaster.

• The challenge is to discover where on the roller coaster the coin will fall when the car is released. For that, the students should calculate the acceleration of the car in different parts of the roller coaster, using the formula for acceleration in uniform circular motion.

• Students should write the calculations and predictions on their sheets of paper. Then, they must test their predictions by releasing the car from the roller coaster and observing where the coin falls.

• The teacher should walk around the room, providing assistance to the groups, and encouraging the discussion of the students' observations and predictions.

3. Activity 3 - "Carnival" (5 - 8 minutes)

• To end the Development phase, the teacher proposes a final challenge. Still in their groups, the students must choose a carnival attraction that involves uniform circular motion (such as Ferris wheels, carousels, teacups, etc.).

• The challenge is to create a short "report" on the attraction, explaining how it works and how the concept of acceleration in uniform circular motion applies to it.

• The students can search the internet, use textbooks, or ask for the teacher's assistance to prepare their report. The teacher should encourage the students to link the concept of acceleration in uniform circular motion with the experience they had when using the chosen attraction.

• The teacher should also highlight the importance of citing the research sources used, and of preparing a well-structured and clear text. This activity fosters the Development of the students' researching, writing, and argumentation skills, as well as consolidating their understanding of the concept of acceleration in uniform circular motion.

Debrief (10 - 12 minutes)

1. Group discussion (3 - 5 minutes)

• The teacher gathers the students in a circle for a group discussion. Each group is invited to share the solutions and conclusions they reached during the activities.

• The teacher must make sure that each student has the opportunity to speak and share their ideas. They should encourage students to explain their responses and to justify their conclusions, fostering an environment of collaborative learning and respect to different opinions.

• During the discussion, the teacher can ask questions to stimulate the critical thinking of students, and to broaden their understanding of the subject. For example: "Why doesn't the angular velocity depend on the radius of the path?" or "What would happen to the car's acceleration if we increased the track's radius?"

2. Connection with the theory (2 - 3 minutes)

• After the discussion, the teacher provides a synthesis of the main ideas discussed, linking them to the theory introduced at the beginning of the lesson. They can highlight the practical applications of the concept of acceleration in uniform circular motion, reinforcing the importance of the subject to everyday life and technology.

• The teacher can also use this time to clarify possible doubts that may have arisen during the practical activities. They must pay attention to students' difficulties and search for strategies to help them overcome them, through examples, analogies, and more detailed explanations when necessary.

3. Individual reflection (3 - 5 minutes)

• The teacher asks the students to reflect individually on what they learned in class. They provide three questions to help with the reflection:

1. What was the most important concept you learned today?

2. What issues still need answering?

3. How can you apply what you learned today in your everyday life?

• Students should write their answers on a sheet of paper. The teacher can collect these responses at the end of class or they can be used at the beginning of the next class, depending on the teacher's plans.

• This individual reflection allows students to consolidate what they have learned in class, identify potential gaps in their knowledge, and realize the relevance of the subject to their lives. Besides, it gives the teacher valuable feedback about the effectiveness of their lesson and the students' learning needs.

Closure (5 - 7 minutes)

1. Summary and Recapitulation (2 - 3 minutes)

• The teacher starts the closure by recapping the main points of the class, summarizing the major concepts and formulas used to calculate the acceleration in uniform circular motion.

• For example, they can highlight that the acceleration in uniform circular motion depends solely on the variation in angular velocity and on the radius of the path, and that the angular velocity is the variation in the angle in relation to time.

• The teacher can also review the practical activities realized, highlighting the results obtained by students and the relations established between theory and practice.

2. Connection between theory, practice, and applications (1 - 2 minutes)

• Then, the teacher stresses the connection between the theory, the practice, and the applications of the concept of acceleration in uniform circular motion.

• They can mention, for example, how the practical activities allowed the students to explore and understand in a more concrete and significant way the proposed theory.

• The teacher can also recall applications of the concept of acceleration in uniform circular motion in the everyday life and in technology, such as carnival attractions, in washing machines, etc.

3. **Supplementary materials (1 - 2 minutes)

• To complement the students' understanding about the subject, the teacher suggests additional studying materials. These can include explanatory videos, interactive simulations, in-depth reading, and extra practice exercises.

• The teacher can recommend students to watch a video on the acceleration in uniform circular motion in amusement parks or to explore an online interactive simulation that allow manipulation of angular velocity and radius of the path.

• They can also indicate a chapter in a Physics textbook that deals with the subject or a list of practice questions so the students can practice applying the formulas of acceleration in uniform circular motion.

4. **Importance of the subject to the daily life (1 minute)

• Finally, the teacher highlights the importance of the concept of acceleration in uniform circular motion for the daily life.

• They can mention that understanding this concept can help with understanding the workings of different technologies present in our daily lives such as washing machines, roller coasters, among others.

• The teacher can also emphasize that besides the practical applications, studying this concept contributes to the development of fundamental skills like problem-solving abilities, critical thinking and teamwork.